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Academic literature on the topic 'Structures Abéliennes'
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Journal articles on the topic "Structures Abéliennes"
Benoist, Franck, and Françoise Delon. "Questions de corps de définition pour les variétés abéliennes en caractéristique positive." Journal of the Institute of Mathematics of Jussieu 7, no. 4 (October 2008): 623–39. http://dx.doi.org/10.1017/s1474748008000145.
Full textDissertations / Theses on the topic "Structures Abéliennes"
Gillibert, Jean. "Invariants de classes pour les variétés abéliennes à réduction semi-stable." Phd thesis, Université de Caen, 2004. http://tel.archives-ouvertes.fr/tel-00011498.
Full textDans le chapitre I, nous étudions les propriétés fonctorielles de ces homomorphismes. Nous en déduisons une généralisation de résultats de Taylor, Srivastav, Agboola et Pappas concernant le noyau du class invariant homomorphism pour les variétés abéliennes ayant partout bonne réduction qui sont isogènes à un produit de courbes elliptiques.
Dans le chapitre II, nous donnons une lecture du class invariant homomorphism dans le langage des 1-motifs.
Dans le chapitre III, nous généralisons la construction du class invariant homomorphism pour un sous-groupe fini et plat d'un schéma en groupes semi-stable (sur un schéma de base intègre, normal et noethérien) dont la fibre générique est une variété abélienne. Nous étendons également les résultats de Taylor, Srivastav, Agboola et Pappas à cette situation.
Dans le chapitre IV, nous généralisons la construction du chapitre III en considérant un sous-groupe fermé, quasi-fini et plat du modèle de Néron d'une variété abélienne (la base étant un schéma de Dedekind). Ceci nous permet de généraliser un résultat arakélovien du à Agboola et Pappas.
Hossain, Akash. "Forking in valued fields and related structures." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM019.
Full textThis thesis is a contribution to the model theory of valued fields. We study forking in valued fields and some of their reducts. We focus particularly on pseudo-local fields, the ultraproducts of residue characteristic zero of the p-adic valued fields. First, we look at the value groups of the valued fields we are interested in, the regular ordered Abelian groups. We establish for these ordered groups a geometric description of forking, as well as a full classification of the global extensions of a given type which are non-forking or invariant. Then, we prove an Ax-Kochen-Ershov principle for forking and dividing in expansions of pure short exact sequences of Abelian structures, as studied by Aschenbrenner-Chernikov-Gehret-Ziegler in their article about distality. This setting applies in particular to the leading-term structure of (expansions of) valued fields. Lastly, we give various sufficient conditions for a parameter set in a Henselian valued field of residue characteristic zero to be an extension base. In particular, we show that forking equals dividing in pseudo-local of residue characteristic zero. Additionally, we discuss results by Ealy-Haskell-Simon on forking in separated extensions of Henselian valued fields of residue characteristic zero. We contribute to the question in the setting of Abhyankar extensions, where we show that, with some additional conditions, if a type in a pseudo-local field does not fork, then there exists some global invariant Keisler measure whose support contains that type. This behavior is well-known in pseudo-finite fields
Stroh, Benoît. "Compactifications de variétés de Siegel aux places de mauvaise réduction." Thesis, Nancy 1, 2008. http://www.theses.fr/2008NAN10109/document.
Full textIn this thesis, we construct compactifications of Siegel modular varieties at bad reduction places of parahoric type. We first construct the toroidal compactifications, which are quite explicit and whose singularities are controlled. These compactifications are not canonical, but depend on some combinatorial choice. The main point in our construction is an approximation of Mumford degenerating abelian varieties that preserves a torsion subgroup. This allows us to glue together the different local charts of the compactifications. We use these results to construct the minimal compactifications, which are canonical but less explicit and more singular. As an application, we give a new proof of the existence of the canonical subgroup for abelian varieties
Bruche, Clément. "Structure galoisienne relative d'anneaux d'entiers d'extensions non abéliennes." Valenciennes, 2007. http://ged.univ-valenciennes.fr/nuxeo/site/esupversions/aa3c8ae9-3fc8-41e3-bfac-dd5f7159a586.
Full textLet k be a number field, Ok its ring of integers and Cl(k) its classgroup. Let G be a finite group, N/k a Galois extension with Galois group isomorphic to G, and ON the ring of integers of N. Let M be a maximal Ok -order in the semi-simple algebra k[G] containing Ok[G], and Cl(M) its classgroup (i. E. The classgroup of locally free M-modules). When N/k is tame (i. E. , at most tamely ramified), extension of scalars allows us to assign to ON the class of M*ON , denoted [M*ON ], in Cl(M). We define the set R(M) of realizable classes to be the set of classes c of Cl(M) such that there exists a Galois extension N/k which is tame, with Galois group isomorphic to G, and for which [M*ON ] = c. It is well known that R(M) is included in Cl◦(M), where Cl◦(M) is the kernel of the morphism from Cl(M) to Cl(k) induced by the augmentation from M to Ok. The results of McCulloh lead one to the following conjecture : R(M) is a subgroup of Cl◦(M). If G is abelian and k is any number field, it follows from the works of McCulloh that this conjecture is true. Let p be a prime number and x a primitive p-th root of unity. In this thesis, assuming x in k, we prove the conjecture when G = V*\rhoC, where V is an Fp -vector space of dimension r ≥ 1, C a cyclic group of order p^r −1, and \rho a faithful representation of C in V ; an example is the symmetric group S3. When we attempt to study this conjecture, we are faced with the embedding problem connected with the Steinitz classes. Another part of this thesis is the study of Steinitz classes of extensions with Galois group isomorphic to V*\rhoC, or to a nonabelian group of order p^3. Keywords : Rings of integers, Galois module structure, Realizable classes, Steinitz classes, Maximal order, Fröhlich’s Hom-description of locally free class groups, Fröhlich-Lagrange resolvent, Embedding problem, Cyclic codes, Primitive polynomials
Antei, Marco. "Extension de torseurs." Thesis, Lille 1, 2008. http://www.theses.fr/2008LIL10056/document.
Full textThe question we try to answer in this thesis is the following: let X be a relative scheme over a discrete valuation ring R and y' a G'-torsor over the generic fibre X' of X. Does it exist an R-group scheme G and a G-torsor Y over X whose generic fibre is isomorphic to the given torsor? We face this problem by means of the fundamental group scheme introduced by Nori for a reduced scheme X complete over a field and then generalized by Gasbarri for an irreducible and reduced scheme faithfully flat over a Dedekind scheme. We prove that the natural morphism f between the fundamental group scheme of X' and the generic fibre of the fundamental group scheme of X is always surjective for the fpqc topology. Moreover we prove that any torsor can be extended iff f is an isomorphism. The firstt two chapters of the thesis are devoted to an introduction of the objects used in the last two chapters. ln particular the tannakian definition of the fundamental group scheme and of the universal torsor of Nori are revisited. ln the third chapter a proof of the results mentioned before is given. The fourth chapter is devoted to a related question: let f be a morphism between two schemes Y and X over a field k.s.t. the direct image F of the structural sheaf of Y is essentially finite, is it possible to defme a Galois cIosure? We prove that the universal torsor associated to the sub-category of the category of essentially finite vector bundles generated by F is the desired Galois closure
Ravoson, Vincent. "([rô],s)-structure bi-hamiltonienne, séparabilité, paires de Lax et intégrabilité." Pau, 1992. http://www.theses.fr/1992PAUUA001.
Full textKhalil, Maya. "Classes de Steinitz, codes cycliques de Hamming et classes galoisiennes réalisables d'extensions non abéliennes de degré p³." Thesis, Valenciennes, 2016. http://www.theses.fr/2016VALE0012/document.
Full textHerreng, Thomas. "Étude de la structure galoisienne des unités dans les corps de nombres." Caen, 2007. http://www.theses.fr/2007CAEN2065.
Full textThe well-known normal basis theorem gives the Galois structure of a Galois number field extension, thus raising the question for arithmetic modules within. This dissertation is concerned with two fundamental such objects, namely the ring of integers and the group of units linked to the class group. We start with recalling the Galois structure of the former. The study of the latter requires different techniques and occupies the major part of the dissertation. At first, using Iwasawa theory, we obtain results on the Galois structure of isotypical components for a certain class of extensions. Susenquently, we construct new groups of units by means of Euler systems and prove that they coincide with the cyclotomic units in some cases
Fidanza, Stéphane. "Rôle(s) du champ de fond antisymétrique en théorie des cordes." Phd thesis, Ecole Polytechnique X, 2003. http://pastel.archives-ouvertes.fr/pastel-00000709.
Full textTerrisse, Robin. "Flux vacua and compactification on smooth compact toric varieties." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSE1144/document.
Full textThe study of flux vacua is a primordial step in the understanding of string compactifications and their phenomenological properties. In presence of flux the internal manifold ceases to be Calabi-Yau, but still admits an SU(3) structure which becomes thus the preferred framework. After introducing the relevant geometrical notions this thesis explores the role that fluxes play in supersymmetric compactification through several approaches. At first consistent truncations of type IIA supergravity are considered. It is shown that fermionic condensates can help support fluxes and generate a positive contribution to the cosmological constant. These truncations thus admit de Sitter vacua which are otherwise extremely difficult to get, if not impossible. The argument is initially performed with dilatini condensates and then improved by suggesting a mechanism to generate gravitini condensates from gravitational instantons. Then the focus shifts towards branes and their behavior under non abelian T-duality. The duals of several D-brane solutions of type II supergravity are computed and the branes are tracked down by investigating the fluxes and the charges they carry. The supersymmetric D2 brane is further studied by checking explicitly the generalized spinor equations and discussing the possibility of a massive deformation. The last chapter gives a systematic construction of SU(3) structures on a wide class of compact toric varieties. The construction defines a sphere bundle on an arbitrary two-dimensional toric variety but also works when the base is Kähler-Einstein
Books on the topic "Structures Abéliennes"
Bullones, Marco A. P. Introduction to Abelian Model Structures and Gorenstein Homological Dimensions. Taylor & Francis Group, 2016.
Find full textBullones, Marco A. P. Introduction to Abelian Model Structures and Gorenstein Homological Dimensions. Taylor & Francis Group, 2016.
Find full textBullones, Marco A. P. Introduction to Abelian Model Structures and Gorenstein Homological Dimensions. Taylor & Francis Group, 2016.
Find full textBullones, Marco A. P. Introduction to Abelian Model Structures and Gorenstein Homological Dimensions. Taylor & Francis Group, 2016.
Find full textIntroduction to Abelian Model Structures and Gorenstein Homological Dimensions. Taylor & Francis Group, 2016.
Find full text