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Research School;Algebraic and Complex Geometry;Lie Theory and Generalizations;Number Theory

Bruhat-Tits theory applies to a semisimple group G, defined over an henselian discretly valued field K, such that G admits a Borel K-subgroup after an extension of K. The construction of the theory goes then by a deep Galois descent argument for the building and also for the parahoric group scheme. In the case of unramified extension, that descent has been achieved by Bruhat-Tits at the end of [BT2]. The tamely ramified case is due to G. Rousseau [R]. Recently, G. Prasad found a new way to investigate the descent part of the theory. This is available in the preprints [Pr1, Pr2] dealing respectively with the unramified case and the tamely ramified case. It is much shorter and the method is based more on fine geometry of the building (e.g. galleries) than algebraic groups techniques. Bruhat-Tits theory applies to a semisimple group G, defined over an henselian discretly valued field K, such that G admits a Borel K-subgroup after an extension of K. The construction of the theory goes then by a deep Galois descent argument for the building and also for the parahoric group scheme. In the case of unramified extension, that descent has been achieved by Bruhat-Tits at the end of [BT2]. The tamely ramified case is due to G. ...

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Documents 51E24 | enregistrements trouvés : 26

Descent in Bruhat-Tits theory Prasad, Gopal | CIRM H Nouveau

Crystallographic groups and their generalisations :workshop Katholieke Universiteit Leuven#Campus Kortrijk#May 26-28 Igodt, Paul ; Abels, Herbert ; Felix, Yves ; Grunewald, Fritz | American Mathematical Society 2000 Nouveau

Géométries à courbure négative ou nulle, groupes discrets et rigiditésGrenoble # 2004 Bessières, L. ; Parreau, Anne ; Rémy, Bertrand | Société Mathématique de France 2009 Nouveau

Bruhat-Tits theory of quasi-split groups Rémy, Bertrand | CIRM H Nouveau

Generalized polygons Van Maldeghem, Hendrik | Birkhäuser Verlag 1998 Nouveau

An algebraic approach to association schemes Zieschang, Paul-hermann | Springer 1996 Nouveau

Buildings Brown, Kenneth S. | Springer 1989 Nouveau

Geometries of small almost simple groups based on maximal subgroups Buekenhout, F. ; Cara, Ph. ; Dehon , M. | Belgian Mathematical Society 1998 Nouveau

Abstract root subgroups and simple groups of Lie-type Timmesfeld, Franz Georg | Birkhäuser Verlag 2001 Nouveau

Geometry of sporadic groups II :representations and amalgams Ivanov, A. A. ; Shpectorov, S. V. | Cambridge University Press 2002 Nouveau

Geometry of sporadic groups I :Petersen and tilde geometries Ivanov, A. A. | Cambridge University Press 1999 Nouveau

Coxeter groups and Hopf algebras Aguiar, Marcelo ; Mahajan, Swapneel | Amercian Mathematical Society 2006 Nouveau

Simple groups of finite Morley rank Altinel, Tuna ; Borovik, Alexandre V. ; Cherlin, Gregory L. | Amercian Mathematical Society 2008 Nouveau

Residually weakly primitive and locally two-transitive geometries for sporadic groups Leemans, Dimitri | Academie Royale De Belgique 2008 Nouveau

"Abstract" homomorphisms of split Kac-Moody groups Caprace, Pierre-Emmanuel | American Mathematical Society 2009 Nouveau

Buildings : Theory and Applications Abramenko, Peter ; Brown, Kenneth S. | Springer 2008 Nouveau

Monoidal functors, species and Hopf algebras Aguiar, Marcelo ; Mahajan, Swapneel | American Mathematical Society 2010 Nouveau

Strasbourg master class on geometry Papadopoulos, Athanase ; A'Campo, N. ; Dal'Bo, F. ; Herrlich, F. ; Korablev, Ph. ; Matveev, S. ; Link, G. ; Marché, J. ; Petronio, C. ; Schroeder, V. | European Mathematical Society 2012 Nouveau

Diagram geometry:related to classical groups and buildings Buekenhout, Francis ; Cohen, Arjeh M. | Springer 2013 Nouveau

Buildings and classical groups Garrett, Paul | Chapman & Hall 1997 Nouveau

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Crystallographic groups and their generalisations :
workshop Katholieke Universiteit Leuven#Campus Kortrijk#May 26-28 Igodt, Paul ; Abels, Herbert ; Felix, Yves ; Grunewald, Fritz | American Mathematical Society 2000 Nouveau

Géométries à courbure négative ou nulle, groupes discrets et rigidités
Grenoble # 2004 Bessières, L. ; Parreau, Anne ; Rémy, Bertrand | Société Mathématique de France 2009 Nouveau

Geometry of sporadic groups II :
representations and amalgams Ivanov, A. A. ; Shpectorov, S. V. | Cambridge University Press 2002 Nouveau

Geometry of sporadic groups I :
Petersen and tilde geometries Ivanov, A. A. | Cambridge University Press 1999 Nouveau

Diagram geometry:
related to classical groups and buildings Buekenhout, Francis ; Cohen, Arjeh M. | Springer 2013 Nouveau