Relevant bibliographies by topics / Cohomology of condensed groups

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

Academic literature on the topic 'Cohomology of condensed groups'

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Published: 14 December 2024

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Journal articles on the topic "Cohomology of condensed groups"

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Rodrigues Jacinto, Joaquín, and Juan Rodríguez Camargo. "Solid locally analytic representations of 𝑝-adic Lie groups." Representation Theory of the American Mathematical Society 26, no. 31 (August 31, 2022): 962–1024. http://dx.doi.org/10.1090/ert/615.

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We develop the theory of locally analytic representations of compact p p -adic Lie groups from the perspective of the theory of condensed mathematics of Clausen and Scholze. As an application, we generalise Lazard’s isomorphisms between continuous, locally analytic and Lie algebra cohomology to solid representations. We also prove a comparison result between the group cohomology of a solid representation and of its analytic vectors.
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Artusa, Marco. "Duality for condensed cohomology of the Weil group of a $p$-adic field." Documenta Mathematica 29, no. 6 (November 26, 2024): 1381–434. http://dx.doi.org/10.4171/dm/977.

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We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a p -adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This allows us to enlarge the local Tate duality to a more general category of non-necessarily discrete coefficients, where it takes the form of a Pontryagin duality between locally compact abelian groups.
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Gähler, Franz, and Johannes Kellendonk. "Cohomology groups for projection tilings of codimension 2." Materials Science and Engineering: A 294-296 (December 2000): 438–40. http://dx.doi.org/10.1016/s0921-5093(00)01171-0.

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FISHER, BENJI N., and DAVID A. RABSON. "Group Cohomology and Quasicrystals I: Classification of Two-Dimensional Space Groups." Ferroelectrics 305, no. 1 (January 2004): 37–40. http://dx.doi.org/10.1080/00150190490462360.

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Conduché, Daniel, Hvedri Inassaridze, and Nick Inassaridze. "Modq cohomology and Tate–Vogel cohomology of groups." Journal of Pure and Applied Algebra 189, no. 1-3 (May 2004): 61–87. http://dx.doi.org/10.1016/j.jpaa.2003.10.025.

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Inassaridze, H. "Non-Abelian Cohomology of Groups." gmj 4, no. 4 (August 1997): 313–31. http://dx.doi.org/10.1515/gmj.1997.313.

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Abstract Following Guin's approach to non-abelian cohomology [Guin, Pure Appl. Algebra 50: 109–137, 1988] and, using the notion of a crossed bimodule, a second pointed set of cohomology is defined with coefficients in a crossed module, and Guin's six-term exact cohomology sequence is extended to a nine-term exact sequence of cohomology up to dimension 2.
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Thomas, C. B. "COHOMOLOGY OF FINITE GROUPS." Bulletin of the London Mathematical Society 29, no. 1 (January 1997): 121–23. http://dx.doi.org/10.1112/blms/29.1.121.

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Hiller, Howard. "Cohomology of Bieberbach groups." Mathematika 32, no. 1 (June 1985): 55–59. http://dx.doi.org/10.1112/s002557930001086x.

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Huebschmann, Johannes. "Cohomology of metacyclic groups." Transactions of the American Mathematical Society 328, no. 1 (January 1, 1991): 1–72. http://dx.doi.org/10.1090/s0002-9947-1991-1031239-1.

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Pirashvili, Mariam. "Symmetric cohomology of groups." Journal of Algebra 509 (September 2018): 397–418. http://dx.doi.org/10.1016/j.jalgebra.2018.05.020.

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Dissertations / Theses on the topic "Cohomology of condensed groups"

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Artusa, Marco. "Sur des théorèmes de dualité pour la cohomologie condensée du groupe de Weil d'un corps p-adique." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0228.

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L’objectif de cette thèse est double. Premièrement, on construit une théorie de cohomologie topologique pour le groupe de Weil d’un corps p-adique. En second lieu, on utilise cette théorie pour prouver des théorèmes de dualité, qui se manifestent sous la forme de la dualité de Pontryagin entre groupes abéliens localement compacts. Ces résultats améliorent des théorèmes de dualité existants et leur confèrent une perspective topologique. De tels objectifs peuvent être atteints grâce aux Mathématiques Condensées, qui fournissent un cadre dans lequel il est possible de faire de l’algèbre avec des objets topologiques. On définit une théorie cohomologique pour les groupes condensés et pro-condensés et on étudie ses propriétés. Ensuite, on applique cela au groupe de Weil d’un corps p-adique, considéré comme un groupe pro-condensé. On démontre que, dans certains cas particuliers, les groupes de cohomologie correspondants sont des groupes abéliens localement compacts de rangs finis. Ceci nous permet d’étendre la dualité locale de Tate à une catégorie plus générale de coefficients non nécessairement discrets, o`u elle prend la forme d’une dualité de Pontryagin entre groupes abéliens localement compacts. Dans la dernière partie de la thèse, on utilise le même cadre pour retrouver une version “à la Weil” de la dualité de Tate avec coefficients dans les variétés abéliennes, et plus généralement dans les 1- motifs, en exprimant ces dualités comme des accouplements parfaits entre groupes abéliens condensés. Pour ce faire, on associe à chaque groupe algébrique, resp. 1-motif, un groupe abélien condensé, resp. un complexe de groupes abéliens condensés, avec une action du groupe de Weil (pro-condensé). On appelle cette association la réalisation de Weil-étale condensée. On montre l’existence d’un accouplement de Poincaré condensé pour les variétés abéliennes, et on prouve une version condensée et “à la Weil” de la dualité de Tate à coefficients dans les variétés abéliennes, qui améliore le résultat correspondant de Karpuk. Enfin, on montre l’existence d’un accouplement de Poincaré condensé pour les 1-motifs. On prouve que cet accouplement est compatible à la filtration par les poids et on démontre un théorème de dualité à coefficients dans les 1- motifs, qui améliore un résultat de Harari-Szamuely
The goal of this thesis is twofold. First, we build a topological cohomology theory for the Weil group of p-adic fields. Secondly, we use this theory to prove duality theorems for such fields, which manifest as Pontryagin duality between locally compact abelian groups. These results improve existing duality theorems and give them a topological flavour. Condensed Mathematics allow us to reach these objectives, providing a framework where it is possible to do algebra with topological objects. We define and study a cohomology theory for condensed groups and pro-condensed groups, and we apply it to the Weil group of a p-adic field, considered as a pro-condensed group. The resulting cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This allows us to enlarge the local Tate duality to a more general category of non-necessarily discrete coefficients, where it takes the form of a Pontryagin duality between locally compact abelian groups. In the last part of the thesis, we use the same framework to recover a Weil-version of the Tate duality with coefficients in abelian varieties and more generally in 1-motives, expressing those dualities as perfect pairings between condensed abelian groups. To do this, we associate to every algebraic group, resp. 1-motive, a condensed abelian group, resp. a complex of condensed abelian groups, with an action of the (pro-condensed) Weil group. We call this association the condensed Weil-´etale realisation. We show the existence of a condensed Poincar´e pairing for abelian varieties and we prove a condensed-Weil version of the Tate duality with coefficients in abelian varieties, which improves the correspondent result of Karpuk. Lastly, we exhibit a condensed Poincar´e pairing for 1-motives. We show that this pairing is compatible with the weight filtration and we prove a duality theorem with coefficients in 1-motives, which improves a result of Harari-Szamuely
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Watson, Toni Aliza. "Twisted cohomology groups." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3929.

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Thesis (M.A.) -- University of Maryland, College Park, 2006.
Thesis research directed by: Dept. of Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Česnavičius, Kęstutis. "Selmer groups as flat cohomology groups." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/90180.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 44-46).
Given a prime number p, Bloch and Kato showed how the p Selmer group of an abelian variety A over a number field K is determined by the p-adic Tate module. In general, the pm1-Selmer group Selpmn A need not be determined by the mod pm Galois representation A[pm]; we show, however, that this is the case if p is large enough. More precisely, we exhibit a finite explicit set of rational primes E depending on K and A, such that Selpm A is determined by A[pm] for all ... In the course of the argument we describe the flat cohomology group ... of the ring of integers of K with coefficients in the pm- torsion A[pm] of the Neron model of A by local conditions for p V E, compare them with the local conditions defining Selm 2A, and prove that A[p't ] itself is determined by A[pm] for such p. Our method sharpens the relationship between Selpm A and ... which was observed by Mazur and continues to work for other isogenies 0 between abelian varieties over global fields provided that deg o is constrained appropriately. To illustrate it, we exhibit resulting explicit rank predictions for the elliptic curve 11A1 over certain families of number fields. Standard glueing techniques developed in the course of the proofs have applications to finite flat group schemes over global bases, permitting us to transfer many of the known local results to the global setting.
by Kęstutis Česnavičius.
Ph. D.
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Clark, Jonathan Owen. "Cohomology of some finite groups." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240535.

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Eastridge, Samuel Vance. "First l^2-Cohomology Groups." Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/52952.

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We want to take a look at the first cohomology group H^1(G, l^2(G)), in particular when G is locally-finite. First, though, we discuss some results about the space H^1(G, C G) for G locally-finite, as well as the space H^1(G, l^2(G)) when G is finitely generated. We show that, although in the case when G is finitely generated the embedding of C G into l^2(G) induces an embedding of the cohomology groups H^1(G, C G) into H^1(G, l^2(G)), when G is countably-infinite locally-finite, the induced homomorphism is not an embedding. However, even though the induced homomorphism is not an embedding, we still have that H^1(G, l^2(G)) neq 0 when G is countably-infinite locally-finite. Finally, we give some sufficient conditions for H^1(G,l^2(G)) to be zero or non-zero.
Master of Science
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QUADRELLI, CLAUDIO. "Cohomology of Absolute Galois Groups." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/56993.

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The main problem this thesis deals with is the characterization of profinite groups which are realizable as absolute Galois groups of fields: this is currently one of the major problems in Galois theory. Usually one reduces the problem to the pro-p case, i.e., one would like to know which pro-p groups occur as maximal pro-p Galois groups, i.e., maximal pro-p quotients of absolute Galois groups. Indeed, pro-p groups are easier to deal with than general profinite groups, yet they carry a lot of information on the whole absolute Galois group. We define a new class of pro-p groups, called Bloch-Kato pro-p group, whose Galois cohomology satisfies the consequences of the Bloch-Kato conjecture. Also we introduce the notion of cyclotomic orientation for a pro-p group. With this approach, we are able to recover new substantial information about the structure of maximal pro-p Galois groups, and in particular on theta-abelian pro-p groups, which represent the "upper bound" of such groups. Also, we study the restricted Lie algebra and the universal envelope induced by the Zassenhaus filtration of a maximal pro-p Galois group, and their relations with Galois cohomology via Koszul duality. Altogether, this thesis provides a rather new approach to maximal pro-p Galois groups, besides new substantial results.
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Leary, Ian James. "The cohomology of certain finite groups." Thesis, University of Cambridge, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386114.

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Kim, Yunhyong. "Smooth cochain cohomology of loop groups." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621575.

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Foster-Greenwood, Briana A. "Hochschild Cohomology and Complex Reflection Groups." Thesis, University of North Texas, 2012. https://digital.library.unt.edu/ark:/67531/metadc149591/.

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A concrete description of Hochschild cohomology is the first step toward exploring associative deformations of algebras. In this dissertation, deformation theory, geometry, combinatorics, invariant theory, representation theory, and homological algebra merge in an investigation of Hochschild cohomology of skew group algebras arising from complex reflection groups. Given a linear action of a finite group on a finite dimensional vector space, the skew group algebra under consideration is the semi-direct product of the group with a polynomial ring on the vector space. Each representation of a group defines a different skew group algebra, which may have its own interesting deformations. In this work, we explicitly describe all graded Hecke algebras arising as deformations of the skew group algebra of any finite group acting by the regular representation. We then focus on rank two exceptional complex reflection groups acting by any irreducible representation. We consider in-depth the reflection representation and a nonfaithful rotation representation. Alongside our study of cohomology for the rotation representation, we develop techniques valid for arbitrary finite groups acting by a representation with a central kernel. Additionally, we consider combinatorial questions about reflection length and codimension orderings on complex reflection groups. We give algorithms using character theory to compute reflection length, atoms, and poset relations. Using a mixture of theory, explicit examples, and calculations using the software GAP, we show that Coxeter groups and the infinite family G(m,1,n) are the only irreducible complex reflection groups for which the reflection length and codimension orders coincide. We describe the atoms in the codimension order for the groups G(m,p,n). For arbitrary finite groups, we show that the codimension atoms are contained in the support of every generating set for cohomology, thus yielding information about the degrees of generators for cohomology.
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Anwar, Muhammad F. "Representations and cohomology of algebraic groups." Thesis, University of York, 2011. http://etheses.whiterose.ac.uk/2032/.

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Let G be a semisimple simply connected linear algebraic group over an algebraically closed field k of characteristic p. In [11], Donkin gave a recursive description for the characters of cohomology of line bundles on the flag variety G/B with G = SL3. In chapter 2 of this thesis we try to give a non recursive description for these characters. In chapter 3, we give the first step of a version of formulae in [11] for G = G2. In his famous paper [7], Demazure introduced certain indecomposable modules and used them to give a short proof of the Borel-Weil-Bott theorem (characteristic zero). In chapter 5 we give the cohomology of these modules. In a recent paper [17], Doty introduces the notion of r−minuscule weight and exhibits a tensor product factorization of a corresponding tilting module under the assumption p >= 2h − 2, where h is the Coxeter number. In chapter 4, we remove the restriction on p and consider some variations involving the more general notion of (p,r)−minuscule weights.
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Books on the topic "Cohomology of condensed groups"

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Adem, Alejandro, and R. James Milgram. Cohomology of Finite Groups. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-06280-7.

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Adem, Alejandro, and R. James Milgram. Cohomology of Finite Groups. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-662-06282-1.

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Cogdell, James W., Günter Harder, Stephen Kudla, and Freydoon Shahidi, eds. Cohomology of Arithmetic Groups. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-95549-0.

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James, Milgram R., ed. Cohomology of finite groups. 2nd ed. Berlin: Springer, 2004.

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James, Milgram R., ed. Cohomology of finite groups. Berlin: Springer-Verlag, 1994.

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Vermani, L. R. Lectures on cohomology of groups. Kurukshetra: Publication Bureau, Kurukshetra University, 1994.

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Lang, Serge. Topics in Cohomology of Groups. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0092624.

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Carlson, Jon F., Lisa Townsley, Luis Valeri-Elizondo, and Mucheng Zhang. Cohomology Rings of Finite Groups. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0215-7.

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Maulik, Davesh. Quantum groups and quantum cohomology. Paris: Société Mathématique de France, 2019.

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Lang, Serge. Topics in cohomology of groups. Berlin: Springer, 1996.

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Book chapters on the topic "Cohomology of condensed groups"

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Jantzen, Jens. "Cohomology." In Representations of Algebraic Groups, 49–64. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/107/04.

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Bump, Daniel. "Cohomology of Grassmannians." In Lie Groups, 517–27. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8024-2_48.

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Bump, Daniel. "Cohomology of Grassmannians." In Lie Groups, 428–37. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4757-4094-3_50.

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Mac Lane, Saunders. "Cohomology of Groups." In Homology, 103–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-62029-4_5.

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Hilton, Peter J., and Urs Stammbach. "Cohomology of Groups." In A Course in Homological Algebra, 184–228. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4419-8566-8_7.

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Halter-Koch, Franz. "Cohomology of groups." In Class Field Theory and L Functions, 87–154. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9780429506574-2.

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Wedhorn, Torsten. "Lie Groups." In Manifolds, Sheaves, and Cohomology, 123–37. Wiesbaden: Springer Fachmedien Wiesbaden, 2016. http://dx.doi.org/10.1007/978-3-658-10633-1_6.

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Koch, Helmut. "Cohomology of Profinite Groups." In Springer Monographs in Mathematics, 21–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04967-9_4.

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Harari, David. "Cohomology of Profinite Groups." In Galois Cohomology and Class Field Theory, 65–78. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43901-9_4.

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Serre, Jean-Pierre. "Cohomology of profinite groups." In Springer Monographs in Mathematics, 1–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-59141-9_1.

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Conference papers on the topic "Cohomology of condensed groups"

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Masuoka, Akira. "Hopf cohomology vanishing via approximation by Hochschild cohomology." In Noncommutative Geometry and Quantum Groups. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-8.

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BONANZINGA, V., and L. SORRENTI. "LEXSEGMENT IDEALS AND SIMPLICIAL COHOMOLOGY GROUPS." In Selected Contributions from the 8th SIMAI Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812709394_0016.

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Venkataramana, T. N. "Cohomology of Arithmetic Groups and Representations." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0100.

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Khalkhali, M., and B. Rangipour. "Cyclic cohomology of (extended) Hopf algebras." In Noncommutative Geometry and Quantum Groups. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-5.

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VENKATESH, AKSHAY. "COHOMOLOGY OF ARITHMETIC GROUPS - FIELDS MEDAL LECTURE." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0014.

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SAKANE, YUSUKE, and TAKUMI YAMADA. "HARMONIC COHOMOLOGY GROUPS ON COMPACT SYMPLECTIC NILMANIFOLDS." In Proceedings of the International Conference on Modern Mathematics and the International Symposium on Differential Geometry. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776419_0014.

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SOMA, TERUHIKO. "THE THIRD BOUNDED COHOMOLOGY AND KLEINIAN GROUPS." In Proceedings of the 37th Taniguchi Symposium. WORLD SCIENTIFIC, 1996. http://dx.doi.org/10.1142/9789814503921_0015.

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LI, JIAN-SHU, and JOACHIM SCHWERMER. "AUTOMORPHIC REPRESENTATIONS AND COHOMOLOGY OF ARITHMETIC GROUPS." In Proceedings of the International Conference on Fundamental Sciences: Mathematics and Theoretical Physics. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811264_0005.

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Sharygin, G. I. "Hopf-type Cyclic Cohomology via the Karoubi Operator." In Noncommutative Geometry and Quantum Groups. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-14.

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Callegaro, Filippo, Davide Moroni, and Mario Salvetti. "Cohomology of Artin groups of type \tildeAn, Bn and applications." In Groups, homotopy and configuration spaces, in honour of Fred Cohen's 60th birthday. Mathematical Sciences Publishers, 2008. http://dx.doi.org/10.2140/gtm.2008.13.85.

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Reports on the topic "Cohomology of condensed groups"

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Holod, Petro I. Geometric Quantization, Cohomology Groups and Intertwining Operators. GIQ, 2012. http://dx.doi.org/10.7546/giq-1-2000-95-104.

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