Introduction To Affine Group Schemes

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Introduction To Affine Group Schemes

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Author : W.C. Waterhouse
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Affine Group Schemes written by W.C. Waterhouse and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Ah Love! Could you and I with Him consl?ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme.

Introduction To Affine Group Schemes

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Author : William C. Waterhouse
language : en
Publisher:
Release Date : 1979

Introduction To Affine Group Schemes written by William C. Waterhouse and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Group schemes (Mathematics). categories.

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 Linear algebraic groups 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.

Introduction To Affine Algebraic Groups

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Author : Gerhard Paul Hochschild
language : en
Publisher:
Release Date : 1971

Introduction To Affine Algebraic Groups written by Gerhard Paul Hochschild and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.

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.

The Geometry Of Schemes

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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06

The Geometry Of Schemes written by David Eisenbud and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-06 with Mathematics categories.

Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Introduction To The Theory Of Schemes

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Author : Yuri I. Manin
language : en
Publisher: Springer
Release Date : 2018-05-15

Introduction To The Theory Of Schemes written by Yuri I. Manin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-15 with Mathematics categories.

This English edition of Yuri I. Manin's well-received lecture notes provides a concise but extremely lucid exposition of the basics of algebraic geometry and sheaf theory. The lectures were originally held in Moscow in the late 1960s, and the corresponding preprints were widely circulated among Russian mathematicians. This book will be of interest to students majoring in algebraic geometry and theoretical physics (high energy physics, solid body, astrophysics) as well as to researchers and scholars in these areas. "This is an excellent introduction to the basics of Grothendieck's theory of schemes; the very best first reading about the subject that I am aware of. I would heartily recommend every grad student who wants to study algebraic geometry to read it prior to reading more advanced textbooks."- Alexander Beilinson

Introduction To Algebraic Geometry And Algebraic Groups

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Author :
language : en
Publisher: Elsevier
Release Date : 1980-01-01

Introduction To Algebraic Geometry And Algebraic Groups written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-01 with Mathematics categories.

Introduction to Algebraic Geometry and Algebraic Groups

Geometric And Topological Aspects Of The Representation Theory Of Finite Groups

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Author : Jon F. Carlson
language : en
Publisher: Springer
Release Date : 2018-10-04

Geometric And Topological Aspects Of The Representation Theory Of Finite Groups written by Jon F. Carlson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-04 with Mathematics categories.

These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.

An Introduction To Algebraic Geometry And Algebraic Groups

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Author : Meinolf Geck
language : en
Publisher: Oxford University Press
Release Date : 2013-03-14

An Introduction To Algebraic Geometry And Algebraic Groups written by Meinolf Geck and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.