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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 20E42 | enregistrements trouvés : 32

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

Seminar on algebraic groups and related finite groupsheld at the institute for advanced study 1968/69 Borel, A. ; Carter, R. ; Curtis, W. D. | Springer-Verlag 1970 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

Tits buildings and the model theory of groups :workshop on ...#Sept. Tent, Katrin | Cambridge University Press 2002 Nouveau

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

Model theory and applications:based on the Euro-conference in model theory and applicationsRavello # may 27 - june 1, 2002 Bélair, L. ; Chatzidakis, Z. ; D'Aquino, P. ; Marker, D. ; Otero, M. ; Point, F. ; Wilkie, A. | ARACNE 2002 Nouveau

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

Point de vue de Berkovich sur l’immeuble et filtrations Mayeux, Arnaud | CIRM H Nouveau

Theory of finite groupsa symposium Brauer, Richard ; Sah, Chih-Han | W. A. Benjamin Inc. 1969 Nouveau

Buildings Brown, Kenneth S. | Springer 1989 Nouveau

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

Property $(T)$ for groups graded by root systems Ershov, Mikhail ; Jaikin-Zapirain, Andrei ; Kassabov, Martin | American Mathematical Society 2017 Nouveau

The structure of spherical buildings Weiss, Richard M. | Princeton University Press 2004 Nouveau

Elements of mathematics :Lie groups and Lie algebras. Chapt. 4-6 Bourbaki, N. | Springer 2002 Nouveau

An algebraic structure for Moufang quadrangles De Medts, Tom | American Mathematical Society 2005 Nouveau

Groupes de Kac-Moody déployés et presque déployés Rémy, Bertrand | Société Mathématique de France 2002 Nouveau

Supersymmetry for mathematicians :an introduction Varadarajan, V. S. | American Mathematical Society 2004 Nouveau

The Coxeter legacy :reflections and projections Chandler, Davis ; Ellers, Erich W. | American Mathematical Society 2006 Nouveau

The generalized triangle inequalities in symetric spaces and buildings with applications to algebra Kapovich, Michael ; Leeb, Bernhard ; Millson, John J. | Amercian Mathematical Society 2008 Nouveau

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

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Seminar on algebraic groups and related finite groups
held at the institute for advanced study 1968/69 Borel, A. ; Carter, R. ; Curtis, W. D. | Springer-Verlag 1970 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

Tits buildings and the model theory of groups :
workshop on ...#Sept. Tent, Katrin | Cambridge University Press 2002 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

Model theory and applications:
based on the Euro-conference in model theory and applications
Ravello # may 27 - june 1, 2002 Bélair, L. ; Chatzidakis, Z. ; D'Aquino, P. ; Marker, D. ; Otero, M. ; Point, F. ; Wilkie, A. | ARACNE 2002 Nouveau

Theory of finite groups
a symposium Brauer, Richard ; Sah, Chih-Han | W. A. Benjamin Inc. 1969 Nouveau

Elements of mathematics :
Lie groups and Lie algebras. Chapt. 4-6 Bourbaki, N. | Springer 2002 Nouveau

Supersymmetry for mathematicians :
an introduction Varadarajan, V. S. | American Mathematical Society 2004 Nouveau

The Coxeter legacy :
reflections and projections Chandler, Davis ; Ellers, Erich W. | American Mathematical Society 2006 Nouveau