Literatura científica selecionada sobre o tema "Schémas en groupes réductifs"
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Artigos de revistas sobre o assunto "Schémas en groupes réductifs"
Douai, Jean-Claude. "Espaces homogènes et arithmétique des schémas en groupes réductifs sur les anneaux de Dedekind". Journal de Théorie des Nombres de Bordeaux 7, n.º 1 (1995): 21–26. http://dx.doi.org/10.5802/jtnb.128.
Texto completo da fonteDigne, François, e Jean Michel. "Groupes réductifs non connexes". Annales scientifiques de l'École normale supérieure 27, n.º 3 (1994): 345–406. http://dx.doi.org/10.24033/asens.1696.
Texto completo da fonteDjebali, Nabila. "Sous-groupes réductifs canoniques de groupes biparaboliques réels". Bulletin des Sciences Mathématiques 154 (agosto de 2019): 64–101. http://dx.doi.org/10.1016/j.bulsci.2019.01.001.
Texto completo da fonteColliot-Thélène, Jean-Louis. "Résolutions flasques des groupes réductifs connexes". Comptes Rendus Mathematique 339, n.º 5 (setembro de 2004): 331–34. http://dx.doi.org/10.1016/j.crma.2004.06.012.
Texto completo da fonteBouaziz, Abderrazak. "Intégrales orbitales sur les groupes de Lie réductifs". Annales scientifiques de l'École normale supérieure 27, n.º 5 (1994): 573–609. http://dx.doi.org/10.24033/asens.1701.
Texto completo da fonteCourtès, François. "Distributions invariantes sur les groupes réductifs quasi-déployés". Canadian Journal of Mathematics 58, n.º 5 (1 de outubro de 2006): 897–999. http://dx.doi.org/10.4153/cjm-2006-037-0.
Texto completo da fonteHenniart, Guy. "Représentations des groupes réductifs p-adiques et de leurs sous-groupes distingués cocompacts". Journal of Algebra 236, n.º 1 (fevereiro de 2001): 236–45. http://dx.doi.org/10.1006/jabr.2000.8497.
Texto completo da fonteGille, Philippe. "Spécialisation de la $R$-équivalence pour les groupes réductifs". Transactions of the American Mathematical Society 356, n.º 11 (13 de janeiro de 2004): 4465–74. http://dx.doi.org/10.1090/s0002-9947-04-03443-9.
Texto completo da fonteVignéras, Marie-France. "Série Principale Modulo p De Groupes Réductifs p-Adiques". Geometric and Functional Analysis 17, n.º 6 (6 de fevereiro de 2008): 2090–112. http://dx.doi.org/10.1007/s00039-007-0646-3.
Texto completo da fonteLafforgue, Vincent. "Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale". Journal of the American Mathematical Society 31, n.º 3 (23 de fevereiro de 2018): 719–891. http://dx.doi.org/10.1090/jams/897.
Texto completo da fonteTeses / dissertações sobre o assunto "Schémas en groupes réductifs"
Li, Shang. "An Equivariant Compactification for Adjoint Reductive Group Schemes". Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM028.
Texto completo da fonteWonderful compactifications of adjoint reductive groups over an algebraically closed field play an important role in algebraic geometry and representation theory. In this thesis, we construct an equivariant com- pactification for adjoint reductive groups over arbitrary base schemes. Our compactifications parameterize classical wonderful compactifications of De Concini and Pro- cesi as geometric fibers. Our construction is based on a variant of the Artin-Weil method of birational group laws, and, in the split case, dose not depend on the existence of the classical wonderful compactification over an algebraically closed field. In particular, our construction gives a new intrinsic construction of wonderful compac- tifications. The Picard group scheme of our compactifi- cations is computed. We also discuss several applications of our compactification in the study of torsors under reductive group schemes
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.
Texto completo da fonteDans 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.
Le, Barbier Michael. "Variétés des réductions des groupes algébriques réductifs". Montpellier 2, 2009. http://www.theses.fr/2009MON20051.
Texto completo da fonteInspired by the construction by S. Mukai of a variety classifying Gauss reductions of a smooth projective quadric, A. Iliev and L. Manivel define the variety of reductions for a simple Jordan algebra. Study of these varieties bring up three new Fano varieties. General interset towards Fano varieties is two-fold: on the first side, their intrinsec geometry is remarkable, an the second side, they play a crucial part in birational geometry. New ones are however seldom found. I generalise this construction to reductive symmetric pairs, study some of their general properties and three small dimension examples. These varieties are projective, quasi-homogenous under the operation of the fixed point group of the symmetric pair. Points in the open orbit are the anisotropic, reductive, maximal subalgebras of the symmetric pair. In the general setup, I explain how the centralizer map, a rational map from the anisotropic space to the variety of reductions, parametrizes a smooth open subset, simplifies the study of combinatorial properties of the orbits in this open subset, and allows to slightly generalise to symmetric-pair's context the well-known description of the irregular locus of simple Lie algebras. I classify linear subspaces of the variety of reductions through a general point, and deduce, for the good cases, the positivity of the anticanonical class of the variety. Among studied examples lie two Fano varieties, one is a smooth 6-fold of index 2, the second is a singular normal 8-fold of index 3
Lee, Ting-Yu. "Les foncteurs de plongement de tores dans les groupes réductifs et leurs propriétés arithmétiques". Paris 6, 2012. http://www.theses.fr/2012PA066235.
Texto completo da fonteIn this thesis, we focus on how to embed a torus T into a reductive group G with respect to a given root datum over a scheme S. This problem also relates to how to embed an étale algebra with involution into a central simple algebra with involution. We approach this problem by defining the embedding functor, and prove that it is a left homogeneous space over S under the automorphism group AutS-grp(G) and a right principal homogeneous space over the scheme of maximal tori under the automorphism group Aut(). Therefore, it is representable. Then we can reformulate the original problem into the problem of existence of the S-points of the embedding functor. In order to fix a connected component of the embedding functor, we define an orientation u of with respect to G. We show that the oriented embedding functor is a homogeneous space under the adjoint action of G. Moreover, we show that over a local field L, the orientation u and the Tits index of G determine the existence of L-points of the oriented embedding functor. We also use the techniques developed in Borovoi's paper to prove that the local-global principle holds for oriented embedding functors in certain cases. Actually, the Brauer-Manin obstruction is the only obstruction to the local-global principle for the oriented embedding functor. Finally, we apply the results of oriented embedding functors to give an alternative proof of Prasad and Rapinchuk's Theorem, and improve Theorem 7. 3 in their paper “Local-Global Principles for Embedding of Fields with Involution into Simple Algebras with Involution”
Renard, David. "Intégrales orbitales tordues sur les groupes de Lie réductifs réels : caractérisation et formule d'inversion". Poitiers, 1996. http://www.theses.fr/1996POIT2322.
Texto completo da fonteGouthier, Bianca. "Actions rationnelles de schémas en groupes infinitésimaux". Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0123.
Texto completo da fonteThis thesis focuses on the study of (rational) actions of infinitesimal group schemes, with a particular emphasis on infinitesimal commutative unipotent group schemes and generically free actions and faithful actions. For any finite k-group scheme G acting rationally on a k-variety X, if the action is generically free then the dimension of Lie(G) is upper bounded by the dimension of the variety. We show that this is the only obstruction when k is a perfect field of positive characteristic and G is infinitesimal commutative trigonalizable. If G is unipotent, we also show that any generically free rational action on X of (any power of) the Frobenius kernel of G extends to a generically free rational action of G on X. Moreover, we give necessary conditions to have faithful rational actions of infinitesimal commutative trigonalizable group schemes on varieties, and (different) sufficient conditions in the unipotent case over a perfect field. Studying faithful group scheme actions on a variety X yields information on representable subgroups of the automorphism group functor AutX of X. For any field k, PGL2,k represents the automorphism group functor of P1 k and thus subgroup schemes of PGL2,k correspond to faithful actions on P1 k. Moreover, PGL2,k(k) coincides with the Cremona group in dimension one, i.e. birational self-maps of P1 k, since any rational self-map of a projective non-singular curve extends to the whole curve. In positive characteristic, the situation is completely different if we consider rational actions of infinitesimal group schemes. Most of the faithful infinitesimal actions on the affine line do not extend to P1 k. If the characteristic of a field k is odd, any infinitesimal subgroup scheme of PGL2,k lifts to SL2,k. This is not true in characteristic 2 and, in this case, we give a complete description, up to isomorphism, of infinitesimal unipotent subgroup schemes of PGL2,k. Finally, we prove a result that gives an explicit description of all infinitesimal commutative unipotent k-group schemes with one-dimensional Lie algebra defined over an algebraically closed field k, showing that there are exactly n non-isomorphic such group schemes of fixed order pn
Vidal, Isabelle. "Contributions à la cohomologie étale des schémas et des log-schémas". Paris 11, 2001. http://www.theses.fr/2001PA112246.
Texto completo da fonteThis work consists of two independent parts. The first one (chaps. I through III) deals with logarithmic geometry. In chap. I we define the logarithmic fundamental group of an fs log scheme and in the proper and log smooth case over the spectrum of a henselian dvr we prove that it satisfies a specialization theorem à la Grothendieck. We then consider a standard logarithmic point s of characteristic p. In chap. II we show that if X is an fs log scheme, separated and of finite type over s, the l-adic Kummer etale cohomology (l different from p) of the log geometric fiber of X finitely generated and endowed with a quasi-unipotent action of the logarithmic inertia, and we study the exponents. In chap. III, for k finite with q elements we define, à la Rapoport, the l-adic Kummer etale semi-simple zeta function of X. We prove it is rational and independent of l. In the proper, log smooth, vertical, Cartier type case we interpret it in terms of log crystalline cohomology and describe its zeroes and poles on the p-adic annuli of radius an integral power of q. .
Sorlin, Karine. "Représentations de Gelfand-Graev et correspondance de Springer dans les groupes réductifs non connexes". Amiens, 2001. http://www.theses.fr/2001AMIE0009.
Texto completo da fonteAbdellatif, Ramla. "Autour des représentations modulo p des groupes réductifs p-adiques de rang 1". Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00651063.
Texto completo da fonteMaccan, Matilde. "Sous-schémas en groupes paraboliques et variétés homogènes en petites caractéristiques". Electronic Thesis or Diss., Université de Rennes (2023-....), 2024. https://ged.univ-rennes1.fr/nuxeo/site/esupversions/2e27fe72-c9e0-4d56-8e49-14fc84686d6c.
Texto completo da fonteThis thesis brings to an end the classification of parabolic subgroup schemes of semisimple groups over an algebraically closed field, focusing on characteristic two and three. First, we present the classification under the assumption that the reduced part of these subgroups is maximal; then we proceed to the general case. We arrive at an almost uniform description: with the exception of a group of type G₂ in characteristic two, any parabolic subgroup scheme is obtained by multiplying reduced parabolic subgroups by kernels of purely inseparable isogenies, then taking the intersection. In conclusion, we discuss some geometric implications of this classification
Livros sobre o assunto "Schémas en groupes réductifs"
Représentations des groupes réductifs p-adiques. [Paris]: Société Mathématique de France, 2010.
Encontre o texto completo da fonteMessing, William. Crystals Associated to Barsotti-Tate Groups: With Applications to Abelian Schemes. Springer London, Limited, 2006.
Encontre o texto completo da fonteWiddows, Dominic. Geometry and Meaning. Center for the Study of Language and Inf, 2004.
Encontre o texto completo da fonteVariance And Duality For Cousin Complexes On Formal Schemes (Contemporary Mathematics). American Mathematical Society, 2005.
Encontre o texto completo da fonteCapítulos de livros sobre o assunto "Schémas en groupes réductifs"
Serre, Jean-Pierre. "Groupes de Grothendieck des schémas en groupes réductifs déployés". In Springer Collected Works in Mathematics, 512–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-37725-9_81.
Texto completo da fonteGille, Philippe. "Groupes réductifs". In Lecture Notes in Mathematics, 17–27. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17272-5_2.
Texto completo da fonte