Abelian Galois Cohomology Of Reductive Groups

Author : Mikhail Borovoi
Publisher : American Mathematical Soc.
Page : 50 pages
File Size : 43,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821806500

Get Book

Abelian Galois Cohomology of Reductive Groups by Mikhail Borovoi Pdf

In this volume, a new functor $H^2_{ab}(K,G)$ of abelian Galois cohomology is introduced from the category of connected reductive groups $G$ over a field $K$ of characteristic $0$ to the category of abelian groups. The abelian Galois cohomology and the abelianization map$ab^1:H^1(K,G) \rightarrow H^2_{ab}(K,G)$ are used to give a functorial, almost explicit description of the usual Galois cohomology set $H^1(K,G)$ when $K$ is a number field.

Author : Roger W. Carter,Meinolf Geck
Publisher : Cambridge University Press
Page : 203 pages
File Size : 43,8 Mb
Release : 1998-09-03
Category : Mathematics
ISBN : 9780521643252

Get Book

Representations of Reductive Groups by Roger W. Carter,Meinolf Geck Pdf

This volume provides a very accessible introduction to the representation theory of reductive algebraic groups.

Author : Stephen Urban Chase,D. K. Harrison,Alex Rosenberg
Publisher : American Mathematical Soc.
Page : 79 pages
File Size : 54,9 Mb
Release : 1969
Category : Commutative rings
ISBN : 9780821812525

Get Book

Galois Theory and Cohomology of Commutative Rings by Stephen Urban Chase,D. K. Harrison,Alex Rosenberg Pdf

Author : David Harari
Publisher : Springer Nature
Page : 336 pages
File Size : 42,9 Mb
Release : 2020-06-24
Category : Mathematics
ISBN : 9783030439019

Get Book

Galois Cohomology and Class Field Theory by David Harari Pdf

This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.

Author : James Arthur,Wilfried Schmid,Peter E. Trapa
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 43,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821843666

Get Book

Representation Theory of Real Reductive Lie Groups by James Arthur,Wilfried Schmid,Peter E. Trapa Pdf

"The representation theory of real reductive groups is still incomplete, in spite of much progress made thus far. The papers in this volume were presented at The AMS-IMS-SIAM Joint Summer Research Conference "Representation Theory of Real Reductive Lie Groups" held in Snowbird, Utah in June 2006, with the aim of elucidating the problems that remain, as well as explaining what tools have recently become available to solve them. They represent a significant improvement in the exposition of some of the most important (and often least accessible) aspects of the literature." "This volume will be of interest to graduate students working in the harmonic analysis and representation theory of Lie groups. It will also appeal to experts working in closely related fields."--BOOK JACKET.

Author : Bhatia Rajendra,Pal Arup,Rangarajan G
Publisher : World Scientific
Page : 4144 pages
File Size : 47,5 Mb
Release : 2011-06-06
Category : Mathematics
ISBN : 9789814462938

Get Book

Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures by Bhatia Rajendra,Pal Arup,Rangarajan G Pdf

ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Author : Anonim
Publisher : World Scientific
Page : 814 pages
File Size : 54,7 Mb
Release : 2011
Category : Electronic
ISBN : 9789814324359

Get Book

Proceedings of the International Congress of Mathematicians 2010 (icm 2010) (in 4 Volumes) - Vol. I: Plenary Lectures and Ceremonies, Vols. Ii-iv: Invited Lectures by Anonim Pdf

Author : Philippe Gille,Arturo Pianzola
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 53,8 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9780821887745

Get Book

Torsors, Reductive Group Schemes and Extended Affine Lie Algebras by Philippe Gille,Arturo Pianzola Pdf

The authors give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that the authors take draws heavily from the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows the authors to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields.

Author : Anonim
Publisher : Academic Press
Page : 273 pages
File Size : 49,8 Mb
Release : 1969
Category : Mathematics
ISBN : 0080873464

Get Book

Cohomology of Groups by Anonim Pdf

Cohomology of Groups

Author : Ronnie Lee,Steven H. Weintraub,Jerome William Hoffman
Publisher : American Mathematical Soc.
Page : 75 pages
File Size : 41,7 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821806203

Get Book

The Siegel Modular Variety of Degree Two and Level Four by Ronnie Lee,Steven H. Weintraub,Jerome William Hoffman Pdf

The Siegel Modular Variety of Degree Two and Level Four is by Ronnie Lee and Steven H. Weintraub: Let $\mathbf M_n$ denote the quotient of the degree two Siegel space by the principal congruence subgroup of level $n$ of $Sp_4(\mathbb Z)$. $\mathbfM_n$ is the moduli space of principally polarized abelian surfaces with a level $n$ structure and has a compactification $\mathbfM^*_n$ first constructed by Igusa. $\mathbfM^*_n$ is an almost non-singular (non-singular for $n> 1$) complex three-dimensional projective variety (of general type, for $n> 3$). The authors analyze the Hodge structure of $\mathbfM^*_4$, completely determining the Hodge numbers $h^{p,q} = \dim H^{p,q}(\mathbfM^*_4)$. Doing so relies on the understanding of $\mathbfM^*_2$ and exploitation of the regular branched covering $\mathbfM^*_4 \rightarrow \mathbfM^*_2$.""Cohomology of the Siegel Modular Group of Degree Two and Level Four"" is by J. William Hoffman and Steven H. Weintraub. The authors compute the cohomology of the principal congruence subgroup $\Gamma_2(4) \subset S{_p4} (\mathbb Z)$ consisting of matrices $\gamma \equiv \mathbf 1$ mod 4. This is done by computing the cohomology of the moduli space $\mathbfM_4$. The mixed Hodge structure on this cohomology is determined, as well as the intersection cohomology of the Satake compactification of $\mathbfM_4$.

Author : Jayce R. Getz
Publisher : Springer Nature
Page : 611 pages
File Size : 44,6 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9783031411533

Get Book

An Introduction to Automorphic Representations by Jayce R. Getz Pdf

Author : Karl H. Hofmann,Paul S. Mostert
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642806704

Get Book

Cohomology Theories for Compact Abelian Groups by Karl H. Hofmann,Paul S. Mostert Pdf

Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again playa role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory. A particularly well understood subclass of compact groups is the class of com pact abelian groups. An added element of elegance is the duality theory, which states that the category of compact abelian groups is completely equivalent to the category of (discrete) abelian groups with all arrows reversed. This allows for a virtually complete algebraisation of any question concerning compact abelian groups. The subclass of compact abelian groups is not so special within the category of compact. groups as it may seem at first glance. As is very well known, the local geometric structure of a compact group may be extremely complicated, but all local complication happens to be "abelian". Indeed, via the duality theory, the complication in compact connected groups is faithfully reflected in the theory of torsion free discrete abelian groups whose notorious complexity has resisted all efforts of complete classification in ranks greater than two.

Author : Alexei Skorobogatov
Publisher : Cambridge University Press
Page : 197 pages
File Size : 50,7 Mb
Release : 2001-07-05
Category : Mathematics
ISBN : 9780521802376

Get Book

Torsors and Rational Points by Alexei Skorobogatov Pdf

This book, first published in 2001, is a complete and coherent exposition of the theory and applications of torsors to rational points.

Author : Ross Lawther,Donna M. Testerman
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 55,7 Mb
Release : 1999
Category : Lie algebras
ISBN : 9780821819661

Get Book

$A_1$ Subgroups of Exceptional Algebraic Groups by Ross Lawther,Donna M. Testerman Pdf

This book is intended for graduate students and research mathematicians interested in group theory and genralizations

Author : Lindsay Childs
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 47,7 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821810774

Get Book

Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders by Lindsay Childs Pdf

This book gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.