Relevant bibliographies by topics / P-adic group

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'P-adic group'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "P-adic group"

1

Roggenkamp, Klaus, and Leonard Scott. "Isomorphisms of p-adic Group Rings." Annals of Mathematics 126, no. 3 (November 1987): 593. http://dx.doi.org/10.2307/1971362.

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KOCH, ALAN, and AUDREY MALAGON. "p-ADIC ORDER BOUNDED GROUP VALUATIONS ON ABELIAN GROUPS." Glasgow Mathematical Journal 49, no. 2 (May 2007): 269–79. http://dx.doi.org/10.1017/s0017089507003680.

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AbstractFor a fixed integer e and prime p we construct the p-adic order bounded group valuations for a given abelian group G. These valuations give Hopf orders inside the group ring KG where K is an extension of $\mathbb{Q} _{p}$ with ramification index e. The orders are given explicitly when G is a p-group of order p or p2. An example is given when G is not abelian.
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3

Külshammer, Burkhard. "Central idempotents in p-adic group rings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 56, no. 2 (April 1994): 278–89. http://dx.doi.org/10.1017/s1446788700034881.

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Eisele, Florian. "The p -adic group ring ofSL2(pf)." Journal of Algebra 410 (July 2014): 421–59. http://dx.doi.org/10.1016/j.jalgebra.2014.01.036.

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Zelenov, E. I. "p-adic Heisenberg group and Maslov index." Communications in Mathematical Physics 155, no. 3 (August 1993): 489–502. http://dx.doi.org/10.1007/bf02096724.

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Oliver, Robert. "Central units in p-adic group rings." K-Theory 1, no. 5 (September 1987): 507–13. http://dx.doi.org/10.1007/bf00536982.

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Gras, Georges. "The p-adic Kummer–Leopoldt constant: Normalized p-adic regulator." International Journal of Number Theory 14, no. 02 (February 8, 2018): 329–37. http://dx.doi.org/10.1142/s1793042118500203.

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The [Formula: see text]-adic Kummer–Leopoldt constant [Formula: see text] of a number field [Formula: see text] is (assuming the Leopoldt conjecture) the least integer [Formula: see text] such that for all [Formula: see text], any global unit of [Formula: see text], which is locally a [Formula: see text]th power at the [Formula: see text]-places, is necessarily the [Formula: see text]th power of a global unit of [Formula: see text]. This constant has been computed by Assim and Nguyen Quang Do using Iwasawa’s techniques, after intricate studies and calculations by many authors. We give an elementary [Formula: see text]-adic proof and an improvement of these results, then a class field theory interpretation of [Formula: see text]. We give some applications (including generalizations of Kummer’s lemma on regular [Formula: see text]th cyclotomic fields) and a natural definition of the normalized [Formula: see text]-adic regulator for any [Formula: see text] and any [Formula: see text]. This is done without analytical computations, using only class field theory and especially the properties of the so-called [Formula: see text]-torsion group [Formula: see text] of Abelian [Formula: see text]-ramification theory over [Formula: see text].
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LEE, Joongul. "Contracted Ideals of $p$-adic Integral Group Rings." Tokyo Journal of Mathematics 43, no. 2 (December 2020): 529–36. http://dx.doi.org/10.3836/tjm/1502179313.

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9

Yu, Kunrui. "p-adic logarithmic forms and group varieties II." Acta Arithmetica 89, no. 4 (1999): 337–78. http://dx.doi.org/10.4064/aa-89-4-337-378.

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10

Hare, Kathryn E., and Maziar Shirvani. "The Semisimplicity Problem for p-Adic Group Algebras." Proceedings of the American Mathematical Society 108, no. 3 (March 1990): 653. http://dx.doi.org/10.2307/2047785.

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Dissertations / Theses on the topic "P-adic group"

1

Wald, Christian. "A p-adic quantum group and the quantized p-adic upper half plane." Doctoral thesis, Humboldt-Universität zu Berlin, 2017. http://dx.doi.org/10.18452/18201.

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Eine Quantengruppe ist eine nichtkommutative und nichtkokommutative Hopfalgebra. In dieser Arbeit konstruieren wir eine Deformation der lokalkonvexen Hopfalgebra der lokalanalytischen Funktionen auf GL(2,O), wobei O hier der Bewertungsring einer endlichen Erweiterung der p-adischen Zahlen ist. Wir zeigen, dass diese Deformation eine nichtkommutative, nichtkokommutative lokalkonvexe Hopfalgebra, also eine p-adische Quantengruppe, ist. Unser Hauptresultat ist, dass das starke Dual dieser Deformation eine Fréchet-Stein Algebra ist. Dies bedeutet, dass das starke Dual ein projektiver Limes von noetherschen Banachalgebren unter rechtsflachen Übergangsabbildungen ist. Im kommutativen Fall wurde dies von P. Schneider und J. Teitelbaum gezeigt. Unser Beweis im nichtkommutativen Fall benutzt Ideen von M. Emerton, der einen alternativen Beweis im kommutativen Fall gefunden hat. Für unseren Beweis beschreiben wir gewisse Vervollständigungen der quanten-einhüllenden Algebra und benutzen die Technik der partiell dividierten Potenzen. Eine wichtige Klasse lokalanalytischer Darstellungen von GL(2,K) wird mithilfe globaler Schnitte von Linienbündeln auf der p-adischen oberen Halbebene konstruiert. Wir konstruieren ein nichtkommutatives Analogon der p-adischen oberen Halbebene, von dem wir erwarten, dass es interessante Darstellungen unserer p-adischen Quantengruppe induziert. Die wichtigsten Hilfsmittel der Konstruktion sind die Maninsche Quantenebene, der Bruhat-Tits Baum für PGL(2,K) und die Theorie der algebraischen Mikrolokalisierung.
A quantum group is a noncommutative noncocommutative Hopf algebra. In this thesis we deform the locally convex Hopf algebra of locally analytic functions on GL(2,O), where O is the valuation ring of a finite extension of the p-adic numbers. We show that this deformation is a noncommutative noncocommutative locally convex Hopf algebra, i.e. a p-adic quantum group. Our main result is that the strong dual of our deformation is a Fréchet Stein algebra, i.e. a projective limit of Noetherian Banach algebras with right flat transition maps. This was shown in the commutative case by P. Schneider and J. Teitelbaum. For our proof in the noncommutative case we use ideas of M. Emerton, who gave an alternative proof of the Fréchet Stein property in the commutative case. For the proof we describe completions of the quantum enveloping algebra and use partial divided powers. An important class of locally analytic representations of GL(2,K) is constructed from global sections of line bundles on the p-adic upper half plane. We construct a noncommutative analogue of an affine version of the p-adic upper half plane which we expect to give rise to interesting representations of our p-adic quantum group. We construct this space by using the Manin quantum plane, the Bruhat-Tits tree for PGL(2,K) and the theory of algebraic microlocalization.
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2

Eisele, Florian [Verfasser]. "Group rings over the p-Adic integers / Florian Eisele." Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2012. http://d-nb.info/1022616773/34.

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3

Chinner, Trinity. "Elliptic Tori in p-adic Orthogonal Groups." Thesis, Université d'Ottawa / University of Ottawa, 2021. http://hdl.handle.net/10393/42759.

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In this thesis, we classify up to conjugacy the maximal elliptic toral subgroups of all special orthogonal groups SO(V), where (q,V) is a 4-dimensional quadratic space over a non-archimedean local field of odd residual characteristic. Our parameterization blends the abstract theory of Morris with a generalization of the practical work performed by Kim and Yu for Sp(4). Moreover, we compute an explicit Witt basis for each such torus, thereby enabling its concrete realization as a set of matrices embedded into the group. This work can be used explicitly to construct supercuspidal representations of SO(V).
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4

Ambrosi, Emiliano. "l-adic,p-adic and geometric invariants in families of varieties." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLX019/document.

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Cette thèse est divisée en huit chapitres. D’abord, dans le Chapitre 1, on présente des résultats et des outils déjà connus qu’on utilisera dans la suite de la thèse. Le Chapitre 2 est consacré à résumer de maniére uniforme les nouveaux résultats présentés dans ce manuscrit.Les six chapitre restants sont originals. Dans les Chapitres 3 et 4 on démontre la chose suivante: soit $f:Yrightarrow X$ un morphisme lisse et prope sur une base $X$ lisse et géométriquament connexe sur un corps infini, finiment engendré et de caractéristique positive. Alors il y a beaucoup de points fermées $xin |X|$ tels que le rang du groupe de Néron-Severi de la fibre géometrique de $f$ en $x$ est le même du groupe de Néron-Severi de la fibre géométrique générique. On preuve ça de la façon suivante: on étudie la spécialisation du faisceau lisse $ell$-adique $R^2f_*Ql(1)$ ($ellneq p$); en suite, on le relit avec la spécialisation du F-isocristal $R^2f_{*,cris}mathcal O_{Y/K}(1)$ en passant par la catégorie des F-isocristaux surconvergents. Au final, la conjecture de Tate varationelle dans la cohomologie cristalline, nous permet de déduire le résultat sur les groupes de Néron-Severi depuis le résultat sur $R^2f_{*,cris}mathcal O_{Y/K}(1)$. Cela étend en caractéristique positive les résultats de Cadoret-Tamagawa et André en caractéristique zero.Les Chapitres 5 et 6 sont consacrés à l’étude des groupes de monodromie des F-isocristaux (sur)convergents. En particulier, les résultats dans le Chapitre 5 sont un travail en common avec Marco D'Addezio. On étude les tores maximaux des groupes de monodromie des F-isocristaux (sur)convergents et on utilise ça pour démontrer un cas particulier d’un conjecture de Kedlaya sur les homomorphismes de $F$-isocristeaux convergents. En utilisant ce cas particulier, on démontre que si $A$ est une variété abélienne sans facteurs d'isogonie isotrivial sur un corps de fonctions $F$ sur $overline{F}_p$, alors le groupe $A(F^{mathrm{perf}})_{tors}$ est fini. Cela peut être considéré comme une extension du théoreme de Lang—Néron et donne une réponse positive a une question d'Esnault. Dans le Chapitre 6, on défini une catégorie $overline Q_p$-linéaire des $F$-isocristeaux surconvergents et les groupes de monodromie de ces objets. En exploitant la théorie des compagnons pour les $F$-isocristeaux surconvergents et les faisceaux lisses, on étudie la théorie de spécialisation de ces groupes de monodromie en transférant les résultats du Chapitre 3 dans ce contexte.Les derniers deux chapitres complètent et affinent les résultats des chapitres précédents. Dans le Chapitre 7, on démontre que la conjecture de Tate pour les diviseurs sur les corps finiment engendrés et de caractéristique $p>0$ est une conséquence de la conjecture de Tate pour les diviseurs sur les corps finis de caractéristique $p>0$. Dans le Chapitre 8, on démontre des résultats de borne uniforme en caractéristique positive pour le groupes de Brauer des formes des variétés qui satisfasse la conjecture de Tate $ell$-adique pour les diviseurs. Cela étend en caractéristique positive un résultat de Orr-Skorobogatov en caractéristique zéro
This thesis is divided in 8 chapters. Chapter ref{chapterpreliminaries} is of preliminary nature: we recall the tools that we will use in the rest of the thesis and some previously known results. Chapter ref{chapterpresentation} is devoted to summarize in a uniform way the new results obtained in this thesis.The other six chapters are original. In Chapters ref{chapterUOIp} and ref{chapterneron}, we prove the following: given a smooth proper morphism $f:Yrightarrow X$ over a smooth geometrically connected base $X$ over an infinite finitely generated field of positive characteristic, there are lots of closed points $xin |X|$ such that the rank of the N'eron-Severi group of the geometric fibre of $f$ at $x$ is the same of the rank of the N'eron-Severi group of the geometric generic fibre. To prove this, we first study the specialization of the $ell$-adic lisse sheaf $R^2f_*Ql(1)$ ($ellneq p$), then we relate it with the specialization of the F-isocrystal $R^2f_{*,crys}mathcal O_{Y/K}(1)$ passing trough the category of overconvergent F-isocrystals. Then, the variational Tate conjecture in crystalline cohomology, allows us to deduce the result on the N'eron-Severi groups from the results on $R^2f_{*,crys}mathcal O_{Y/K}(1)$. These extend to positive characteristic results of Cadoret-Tamagawa and Andr'e in characteristic zero.Chapters ref{chaptermarcuzzo} and ref{chapterpadic} are devoted to the study of the monodromy groups of (over)convergent F-isocrystals. Chapter ref{chaptermarcuzzo} is a joint work with Marco D'Addezio. We study the maximal tori in the monodromy groups of (over)convergent F-isocrystals and using them we prove a special case of a conjecture of Kedlaya on homomorphism of convergent $F$-isocrystals. Using this special case, we prove that if $A$ is an abelian variety without isotrivial geometric isogeny factors over a function field $F$ over $overline{F}_p$, then the group $A(F^{mathrm{perf}})_{tors}$ is finite. This may be regarded as an extension of the Lang--N'eron theorem and answer positively to a question of Esnault. In Chapter ref{chapterpadic}, we define $overline Q_p$-linear category of (over)convergent F-isocrystals and the monodromy groups of their objects. Using the theory of companion for overconvergent F-isocrystals and lisse sheaves, we study the specialization theory of these monodromy groups, transferring the result of Chapter ref{chapterUOIp} to this setting via the theory of companions.The last two chapters are devoted to complements and refinement of the results in the previous chapters. In Chapter ref{chaptertate}, we show that the Tate conjecture for divisors over finitely generated fields of characteristic $p>0$ follows from the Tate conjecture for divisors over finite fields of characteristic $p>0$. In Chapter ref{chapterbrauer}, we prove uniform boundedness results for the Brauer groups of forms of varieties in positive characteristic, satisfying the $ell$-adic Tate conjecture for divisors. This extends to positive characteristic a result of Orr-Skorobogatov in characteristic zero
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Feldmann, Mark [Verfasser], and Peter [Akademischer Betreuer] Schneider. "p-adic Weil group representations / Mark Feldmann ; Betreuer: Peter Schneider." Münster : Universitäts- und Landesbibliothek Münster, 2018. http://d-nb.info/1168324815/34.

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6

Vaintrob, Dmitry. "Mirror symmetry and the K theory of a p-adic group." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104578.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 59-61).
Let G be a split, semisimple p-adic group. We construct a derived localization functor Loc : ... from the compactified category of [BK2] associated to G to the category of equivariant sheaves on the Bruhat-Tits building whose stalks have finite-multiplicity isotypic components as representations of the stabilizer. Our construction is motivated by the "coherent-constructible correspondence" functor in toric mirror symmetry and a construction of [CCC]. We show that Loc has a number of useful properties, including the fact that the sections ... compactifying the finitely-generated representation V. We also construct a depth by Dmitry A. Vaintrob.
Ph. D.
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7

Wald, Christian [Verfasser], Elmar [Gutachter] Große-Klönne, Joachim [Gutachter] Mahnkopf, and Tobias [Gutachter] Schmidt. "A p-adic quantum group and the quantized p-adic upper half plane / Christian Wald ; Gutachter: Elmar Große-Klönne, Joachim Mahnkopf, Tobias Schmidt." Berlin : Humboldt-Universität zu Berlin, 2017. http://d-nb.info/118932816X/34.

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Schoemann, Claudia. "Représentations unitaires de U(5) p-adique." Thesis, Montpellier 2, 2014. http://www.theses.fr/2014MON20101.

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Nous étudions les représentations complexes, induites par l'induction parabolique, du groupe U(5), défini sur un corps local non-archimedean de caractéristique 0. C'est Qp ou une extension finie de Qp .On parle des 'corps p-adiques'. Soit F un corps p-adique. Soit E : F une extension de corps de degré 2. Soit Gal(E : F ) = {id, σ}le groupe de Galois. On écrit σ(x) = overline{x} forall x ∈ E. Soit | |p la norme p-adique de E. Soient E* = E {0} et E 1 = {x ∈ E | xoverline{x}= 1} .U (5) a trois sous-groupes paraboliques propres. Soit P0 le sous-groupe parabolique minimal et soientP1 et P2 les deux sous-groupes paraboliques maximaux. Soient M0 , M1 et M2 les sous-groupes de Levi standards et soient N0 , N1 et N2 des sous-groupes unipotents de U (5). On a la décomposition de Levi Pi = Mi Ni , i ∈{0, 1, 2} .M0 = E* × E* × E 1 est le sous-groupe de Levi minimal, M1 = GL(2, E) × E 1 et M2 = E* × U(3) sont les sous-groupes de Levi maximaux.On considère les représentations des sous-groupes de Levi, et on les étend trivialement au sous-groupes unipotents pour obtenir des représentations des sous-groupes paraboliques. On exécute une procédure appelée 'l'induction parabolique' pour obtenir les représentations de U (5). Nous considérons les représentations de M0 , puis les représentations non-cuspidales, induites à partir de M1 et M2 . Cela veut dire que la représentation du facteur GL(2, E) de M1 est un sous-quotient propre d'une représentation induite de E* × E* à GL(2, E). La représentation du facteur U (3) de M2 est un sous-quotient propre d'une représentation induite de E* × E 1 à U(3). Un exemple pour M1 est | det |α χ(det) StGL2 * λ' , où α ∈ R, χ est un caractère unitaire de E* , StGL2 est la représentation Steinberg de GL(2, E) et λ' est un caractère de E 1 . Un exemple pour M2 est| |α χ λ (det) StU (3) , où α ∈ R, χ est un caractère unitaire de E* , λ' est un caractère unitaire de E 1et StU (3) est la représentation Steinberg de U(3). On remarque que λ' est unitaire.Ensuite on considère les représentations cuspidales de M1 .On détermine les droites et les points de réductibilité des représentations de U(5) et on détermine les sous-quotients irréductibles. Ensuite, sauf quelque cas particuliers, on détermine le dual unitaire de U(5)par rapport au quotients de Langlands. Les représentations complexes, paraboliquement induites, de U(3) sur un corps p-adique sont classifiées par Charles David Keys dans [Key84], les représentations complexes, paraboliquement induites, de U(4)sur un corps p-adique sont classifiées par Kazuko Konno dans [Kon01]
We study the parabolically induced complex representations of the unitary group in 5 variables - U(5)- defined over a non-archimedean local field of characteristic 0. This is Qp or a finite extension of Qp ,where p is a prime number. We speak of a 'p-adic field'.Let F be a p-adic field. Let E : F be a field extension of degree two. Let Gal(E : F ) = {id, σ}. We write σ(x) = overline{x} forall x ∈ E. Let | |p denote the p-adic norm on E. Let E* := E {0} and let E 1 := {x ∈ E | x overline{x} = 1} .U(5) has three proper parabolic subgroups. Let P0 denote the minimal parabolic subgroup and P1 andP2 the two maximal parabolic subgroups. Let M0 , M1 and M2 denote the standard Levi subgroups and let N0 , N1and N2 denote unipotent subgroups of U(5). One has the Levi decomposition Pi = Mi Ni , i ∈ {0, 1, 2} .M0 = E* × E* × E 1 is the minimal Levi subgroup, M1 = GL(2, E) × E 1 and M2 = E* × U (3) are the two maximal parabolic subgroups.We consider representations of the Levi subgroups and extend them trivially to the unipotent subgroups toobtain representations of the parabolic groups. One now performs a procedure called 'parabolic induction'to obtain representations of U (5).We consider representations of M0 , further we consider non-cuspidal, not fully-induced representationsof M1 and M2 . For M1 this means that the representation of the GL(2, E)− part is a proper subquotientof a representation induced from E* × E* to GL(2, E). For M2 this means that the representation of theU (3)− part of M2 is a proper subquotient of a representation induced from E* × E 1 to U (3).As an example for M1 , take | det |α χ(det) StGL2 * λ' , where α ∈ R, χ is a unitary character of E* , StGL2 is the Steinberg representation of GL(2, E) and λ' is a character of E 1 . As an example forM2 , take | |α χ λ' (det) StU (3) , where α ∈ R, χ is a unitary character of E* , λ' is a character of E 1 andStU (3) is the Steinberg representation of U (3). Note that λ' is unitary.Further we consider the cuspidal representations of M1 .We determine the points and lines of reducibility of the representations of U(5), and we determinethe irreducible subquotients. Further, except several particular cases, we determine the unitary dual ofU(5) in terms of Langlands-quotients.The parabolically induced complex representations of U(3) over a p-adic field have been classied byCharles David Keys in [Key84], the parabolically induced complex representations of U(4) over a p-adicfield have been classied by Kazuko Konno in [Kon01].An aim of further study is the classication of the induced complex representations of unitary groupsof higher rank, like U (6) or U (7). The structure of the Levi subgroups of U (6) resembles the structureof the Levi subgroups of U (4), the structure of the Levi groups of U (7) resembles those of U (3) and ofU (5).Another aim is the classication of the parabolically induced complex representatioins of U (n) over ap-adic field for arbitrary n. Especially one would like to determine the irreducible unitary representations
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Ludsteck, Thomas. "P-adic vector bundles on curves and abelian varieties and representations of the fundamental group." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-35588.

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Csige, Tamás. "K-theoretic methods in the representation theory of p-adic analytic groups." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2017. http://dx.doi.org/10.18452/17697.

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Sei G eine p-adische analytische gruppe, welche die direkte Summe einer torsionfreien p-adische analytische gruppe H mit zerfallender halbeinfacher Liealgebra und einer n-dimensionalen abelschen p-adische analytische gruppe Z ist. In Kapitel 3 zeigen wir folgenden Satz: Sei M ein endlich erzeugter Torsionmodul über der Iwasawaalgebra von G, welcher keine nichtrivialen pseudo-null-Untermoduln besitzt. Dann ist q(M), das Bild von M in der Quotientenkategorie Q, genau dann volltreu, wenn M als Modul über der Iwasawaalgebra von Z torsionsfrei ist. Hierbei bezeichne Q den Serre-Quotienten der Kategorie der Moduln über der Iwasawaalgebra von G nach der Serre-Unterkategorie der pseudo-null-Moduln. In Kapitel 4 zeigen wir folgenden Satz: Es bezeichne T die Kategorie, deren Objekte die endlich erzeugten Modulen über der Iwasawaalgebra von G sind, welche auch als Moduln über der Iwasawaalgebra von H endlich erzeugt sind. Seien M, N zwei Objekte von T. Wir nehmen an, dass M, N keine nichttrivialen pseudo-null-Untermoduln besitzen und q(M) in Q volltreu ist. Dann gilt: Ist [M]=[N] in der Grothendieckgruppe von Q, so ist das Bild von N ebenfalls volltreu. In Kapitel 5 zeugen wir folgenden Satz: Sei G eine beliebige p-adische analytische Gruppe, welche keine Element der Ordung p besitzt. Dann sind die Grothendieckgruppen der Algebra stetiger Distributionen und der Algebra beschränkter Distributionen isomorph zu c Kopien des Rings der ganzen Zahlen, wobei c die Anzahl der p-regulären Konjugationsklassen des Quotienten von G nach einer offenen uniformen pro-p-Untergruppe H bezeichnet.
Let G be a compact p-adic analytic group with no element of order p such that it is the direct sum of a torsion free compact p-adic analytic group H whose Lie algebra is split semisimple and an abelian p-adic analytic group Z of dimension n. In chapter 3, we show that if M is a finitely generated torsion module over the Iwasawa algebra of G with no non-zero pseudo-null submodule, then the image q(M) of M via the quotient functor q is completely faithful if and only if M is torsion free over the Iwasawa algebra of Z. Here the quotient functor q is the unique functor from the category of modules over the Iwasawa algebra of G to the quotient category with respect to the Serre subcategory of pseudo-null modules. In chapter 4, we show the following: Let M, N be two finitely generated modules over the Iwasawa algebra of G such that they are objects of the category Q of those finitely generated modules over the Iwasaw algebra of G which are also finitely generated as modules over the Iwasawa algebra of H. Assume that q(M) is completely faithful and [M] =[N] in the Grothendieck group of Q. Then q(N) is also completely faithful. In chapter 6, we show that if G is any compact p-adic analytic group with no element of order p, then the Grothendieck groups of the algebras of continuous distributions and bounded distributions are isomorphic to c copies of the ring of integers where c denotes the number of p-regular conjugacy classes in the quotient group of G with an open normal uniform pro-p subgroup H of G.
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Books on the topic "P-adic group"

1

Eng-chye, Tan, and Zhu Chen-bo, eds. Representations of real and p-adic groups. Singapore: Singapore University Press, 2004.

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2

1976-, Berger Laurent, Breuil Christophe, and Colmez Pierre, eds. Représentations p-adiques de groupes p-adiques I: Représentations galoisiennes et ([phi, gamma])-modules. Paris, France: Société mathématique de France, 2008.

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Rapoport, M. Period spaces for p-divisible groups. Princeton, N.J: Princeton University Press, 1996.

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4

Marcus, Du Sautoy, Segal Daniel Ph D, and Shalev Aner 1958-, eds. New horizons in pro-p groups. Boston: Birkhäuser, 2000.

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5

Klaas, G. Linear pro-p-groups of finite width. Berlin: Springer, 1997.

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6

1937-, Doran Robert S., Sally Paul, and Spice Loren 1981-, eds. Harmonic analysis on reductive, p-adic groups: AMS Special Session on Harmonic Analysis and Representations of Reductive, p-adic Groups, January 16, 2010, San Francisco, CA. Providence, R.I: American Mathematical Society, 2011.

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7

Schneider, Peter. p-Adic Lie Groups. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21147-8.

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service), SpringerLink (Online, ed. p-Adic Lie Groups. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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Alain, Genestier, Lafforgue Vincent, and SpringerLink (Online service), eds. L'isomorphisme entre les tours de Lubin-Tate et de Drinfeld. Basel: Birkhäuser, 2008.

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Représentations des groupes réductifs p-adiques. [Paris]: Société Mathématique de France, 2010.

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Book chapters on the topic "P-adic group"

1

Berndt, Rolf, and Ralf Schmidt. "Local Representations: The p-adic Case." In Elements of the Representation Theory of the Jacobi Group, 105–36. Basel: Springer Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-0283-3_5.

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Abbes, Ahmed, and Michel Gros. "Chapter I. Representations of the fundamental group and the torsor of deformations. An overview." In The p-adic Simpson Correspondence, 1–26. Princeton: Princeton University Press, 2016. http://dx.doi.org/10.1515/9781400881239-002.

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Abbes, Ahmed, and Michel Gros. "Chapter II. Representations of the fundamental group and the torsor of deformations. Local study." In The p-adic Simpson Correspondence, 27–178. Princeton: Princeton University Press, 2016. http://dx.doi.org/10.1515/9781400881239-003.

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Abbes, Ahmed, and Michel Gros. "Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects." In The p-adic Simpson Correspondence, 179–306. Princeton: Princeton University Press, 2016. http://dx.doi.org/10.1515/9781400881239-004.

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Clozel, Laurent. "Invariant Harmonic Analysis on the Schwartz Space of a Reductive p-ADIC Group." In Progress in Mathematics, 101–21. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0455-8_6.

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Fernández-Alcober, Gustavo A., Olivier Siegenthaler, and Amaia Zugadi-Reizabal. "Hausdorff Dimension and the Abelian Group Structure of Some Groups Acting on the p-Adic Tree." In Trends in Mathematics, 39–43. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05488-9_7.

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Vignéras, Marie-France. "Irreducible Modular Representations of a Reductive p-Adic Group and Simple Modules for Hecke Algebras." In European Congress of Mathematics, 117–33. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8268-2_7.

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Garrett, Paul. "Lattices, p-adic Numbers, Discrete Valuations." In Buildings and Classical Groups, 305–20. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5340-9_18.

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Vourdas, Apostolos. "p-adic Numbers and Profinite Groups." In Quantum Science and Technology, 145–60. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59495-8_10.

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Symonds, Peter, and Thomas Weigel. "Cohomology of p-adic Analytic Groups." In New Horizons in pro-p Groups, 349–410. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1380-2_12.

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Conference papers on the topic "P-adic group"

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Tadić, Marko. "Reducibility and discrete series in the case of classical p-adic groups; an approach based on examples." In Proceedings of the International Symposium in Honor of Takayuki Oda on the Occasion of His 60th Birthday. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814355605_0010.

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Kusumaningtyas, Mei, and Hana Kristina. "The Relative Effectivness of Steady State Cardio and High Intensity Interval Training on Cardiorespiratory Fitness Among Students at School of Health Polytechnics, Surakarta." In The 7th International Conference on Public Health 2020. Masters Program in Public Health, Universitas Sebelas Maret, 2020. http://dx.doi.org/10.26911/the7thicph.05.08.

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Abstract:
ABSTRACT Background: Cardiorespiratory fitness essential to prevent the risk cardiovascular disease. This study aimed to determine the relative effectiveness of Steady State Cardio (SSC) and High-Intensity Interval Training (HIIT) on cardiorespiratory fitness in the early adult age group. Subjects and Method: This was a randomized control trial conducted at the School of Health Polytechnics, Surakarta, from October to November, 2019. A total sample 45 students was divided into 2 groups: (1) SSC group and (2) HIIT group. The dependent variable was cardiorespiratory fitness. The independent variables were SSC and HIIT. The measuring instrument was a multi-stage fitness involving a 20 meter long run. The results were converted into VO2max level. The data were analyzed by Mann Whitney. Results: After the intervention, the VO2max level was higher in the HIIT group (Mean= 24.28; SD= 5.42) than the SSC group (Mean= 21.66; SD= 6.99), but it was statistically non-significant (p= 0.503). Conclusion: Steady State Cardio and High Intensity Interval Training have comparable effect on cardiorespiratory fitness. Keywords: high intensity interval training, steady state cardio, cardiorespiratory fitness, VO2max Correspondence: Mei Kusumaningtyas. School of Health Polytechnics, Surakarta. Jl. Adi Sumarmo, Tohudan, Colomadu, Karanganyar, Indonesia. Email: meikusumaningtyas@gmail.com. Mobile: 085725646444 DOI: https://doi.org/10.26911/the7thicph.05.08
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