Classification Of Pseudo Reductive Groups

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Classification Of Pseudo Reductive Groups

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

Classification Of Pseudo Reductive Groups 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.

Classification Of Pseudo Reductive Groups

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Author : Brian Conrad
language : en
Publisher: Princeton University Press
Release Date : 2016

Classification Of Pseudo Reductive Groups 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 2016 with Mathematics categories.

Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To make the continued success of the series, all hooks are again available in paperback. For a complete list of titles, please visit the Princeton University Press website: press.princeton.edu.

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

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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.

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 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.

Bruhat Tits Theory

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Author : Tasho Kaletha
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-26

Bruhat Tits Theory written by Tasho Kaletha 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 2023-01-26 with Mathematics categories.

Comprehensive treatment of Bruhat-Tits theory for graduate students and researchers in number theory, representation theory, and algebraic geometry.

Berkovich Spaces And Applications

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Author : Antoine Ducros
language : en
Publisher: Springer
Release Date : 2014-11-21

Berkovich Spaces And Applications written by Antoine Ducros and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-21 with Mathematics categories.

We present an introduction to Berkovich’s theory of non-archimedean analytic spaces that emphasizes its applications in various fields. The first part contains surveys of a foundational nature, including an introduction to Berkovich analytic spaces by M. Temkin, and to étale cohomology by A. Ducros, as well as a short note by C. Favre on the topology of some Berkovich spaces. The second part focuses on applications to geometry. A second text by A. Ducros contains a new proof of the fact that the higher direct images of a coherent sheaf under a proper map are coherent, and B. Rémy, A. Thuillier and A. Werner provide an overview of their work on the compactification of Bruhat-Tits buildings using Berkovich analytic geometry. The third and final part explores the relationship between non-archimedean geometry and dynamics. A contribution by M. Jonsson contains a thorough discussion of non-archimedean dynamical systems in dimension 1 and 2. Finally a survey by J.-P. Otal gives an account of Morgan-Shalen's theory of compactification of character varieties. This book will provide the reader with enough material on the basic concepts and constructions related to Berkovich spaces to move on to more advanced research articles on the subject. We also hope that the applications presented here will inspire the reader to discover new settings where these beautiful and intricate objects might arise.

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.