Pseudo Reductive Groups

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Pseudo Reductive Groups

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Author : Brian Conrad
language : en
Publisher: Cambridge University Press
Release Date : 2015-06-04

Pseudo Reductive Groups written by Brian Conrad and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-04 with Mathematics categories.

This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. This second edition has been revised and updated, with Chapter 9 being completely rewritten via the useful new notion of 'minimal type' for pseudo-reductive groups.

Classification Of Pseudo Reductive Groups Am 191

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Author : Brian Conrad
language : en
Publisher: Princeton University Press
Release Date : 2015-11-10

Classification Of Pseudo Reductive Groups Am 191 written by Brian Conrad and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-10 with Mathematics categories.

In the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups. In this new book, Classification of Pseudo-reductive Groups, Conrad and Prasad go further to study the classification over an arbitrary field. An isomorphism theorem proved here determines the automorphism schemes of these groups. The book also gives a Tits-Witt type classification of isotropic groups and displays a cohomological obstruction to the existence of pseudo-split forms. Constructions based on regular degenerate quadratic forms and new techniques with central extensions provide insight into new phenomena in characteristic 2, which also leads to simplifications of the earlier work. A generalized standard construction is shown to account for all possibilities up to mild central extensions. The results and methods developed in Classification of Pseudo-reductive Groups will interest mathematicians and graduate students who work with algebraic groups in number theory and algebraic geometry in positive characteristic.

Pseudo Reductive Groups

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Author : Brian Conrad
language : en
Publisher: Cambridge University Press
Release Date : 2010-07-29

Pseudo Reductive Groups written by Brian Conrad and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-29 with Mathematics categories.

Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This self-contained monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. The authors present numerous new results and also give a complete exposition of Tits' structure theory of unipotent groups. They prove the conjugacy results (conjugacy of maximal split tori, minimal pseudo-parabolic subgroups, maximal split unipotent subgroups) announced by Armand Borel and Jacques Tits, and also give the Bruhat decomposition, of general smooth connected algebraic groups. Researchers and graduate students working in any related area, such as algebraic geometry, algebraic group theory, or number theory, will value this book as it develops tools likely to be used in tackling other problems.

Representations Of Algebraic Groups

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Author : Jens Carsten Jantzen
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Representations Of Algebraic Groups written by Jens Carsten Jantzen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.

Classification Of Pseudo Reductive Groups

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Author : Brian Conrad
language : en
Publisher:
Release Date : 1940

Classification Of Pseudo Reductive Groups written by Brian Conrad and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1940 with Geometry, Algebraic categories.

Introduction To Complex Reflection Groups And Their Braid Groups

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Author : Michel Broué
language : en
Publisher: Springer
Release Date : 2010-01-28

Introduction To Complex Reflection Groups And Their Braid Groups written by Michel Broué and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-28 with Mathematics categories.

This book covers basic properties of complex reflection groups, such as characterization, Steinberg theorem, Gutkin-Opdam matrices, Solomon theorem and applications, including the basic findings of Springer theory on eigenspaces.

Algebraic Groups Structure And Actions

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Author : Mahir Bilen Can
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-06

Algebraic Groups Structure And Actions written by Mahir Bilen Can and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-06 with Mathematics categories.

This volume contains the proceedings of the 2015 Clifford Lectures on Algebraic Groups: Structures and Actions, held from March 2–5, 2015, at Tulane University, New Orleans, Louisiana. This volume consists of six articles on algebraic groups, including an enhanced exposition of the classical results of Chevalley and Rosenlicht on the structure of algebraic groups; an enhanced survey of the recently developed theory of pseudo-reductive groups; and an exposition of the recently developed operational -theory for singular varieties. In addition, there are three research articles containing previously unpublished foundational results on birational automorphism groups of algebraic varieties; solution of Hermite-Joubert problem over -closed fields; and cohomological invariants and applications to classifying spaces. The old and new results presented in these articles will hopefully become cornerstones for the future development of the theory of algebraic groups and applications. Graduate students and researchers working in the fields of algebraic geometry, number theory, and representation theory will benefit from this unique and broad compilation of fundamental results on algebraic group theory.

Algebraic Groups

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Author : J. S. Milne
language : en
Publisher: Cambridge University Press
Release Date : 2017-09-21

Algebraic Groups written by J. S. Milne and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-21 with Mathematics categories.

Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

Algebraic Groups And Number Theory

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Author : Vladimir Petrovich Platonov
language : en
Publisher: Cambridge University Press
Release Date : 2023-09-07

Algebraic Groups And Number Theory written by Vladimir Petrovich Platonov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-07 with Mathematics categories.

The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.

Algebraic Groups And Number Theory Volume 1

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Author : Vladimir Platonov
language : en
Publisher: Cambridge University Press
Release Date : 2023-09-07

Algebraic Groups And Number Theory Volume 1 written by Vladimir Platonov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-07 with Mathematics categories.

The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.