The Local Langlands Conjecture for GL(2): Grundlehren der mathematischen Wissenschaften, cartea 335
Autor Colin J. Bushnell, Guy Henniarten Limba Engleză Hardback – 2 aug 2006
This conjecture has now been proved for all F and n, but the arguments are long and rely on many deep ideas and techniques. This book gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groupsand the structure theory of local fields. It uses only local methods, with no appeal to harmonic analysis on adele groups.
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Specificații
ISBN-13: 9783540314868
ISBN-10: 3540314865
Pagini: 368
Ilustrații: XII, 351 p.
Dimensiuni: 155 x 235 x 25 mm
Greutate: 0.66 kg
Ediția:2006
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Grundlehren der mathematischen Wissenschaften
Locul publicării:Berlin, Heidelberg, Germany
ISBN-10: 3540314865
Pagini: 368
Ilustrații: XII, 351 p.
Dimensiuni: 155 x 235 x 25 mm
Greutate: 0.66 kg
Ediția:2006
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Grundlehren der mathematischen Wissenschaften
Locul publicării:Berlin, Heidelberg, Germany
Public țintă
ResearchCuprins
Smooth Representations.- Finite Fields.- Induced Representations of Linear Groups.- Cuspidal Representations.- Parametrization of Tame Cuspidals.- Functional Equation.- Representations of Weil Groups.- The Langlands Correspondence.- The Weil Representation.- Arithmetic of Dyadic Fields.- Ordinary Representations.- The Dyadic Langlands Correspondence.- The Jacquet-Langlands Correspondence.
Recenzii
From the reviews:
"In this book the authors present a complete proof of the Langlands conjecture for GL (2) over a non-archimedean local field, which uses local methods and is accessible to students. … The book is very well written and easy to read." (J. G. M. Mars, Zentralblatt MATH, Vol. 1100 (2), 2007)
"The book under review gives a complete and self-contained insight into the theory of representations of G. … We highly recommend this book to Ph.D. students as well as to specialists. The book contains a huge amount of information, definition and facts … . The book has a Bibliography containing 91 references … ." (Alexandru Ioan Badulescu, Mathematical Reviews, Issue 2007 m)
“The aim of this monograph is to present a complete and self-contained proof of the Langlands conjecture for GL(2) over a non-archimedean local field. … This volume presents a large amount of difficult material in a clear and readable manner. It can be recommended to anyone interested in representations of linear algebraic groups.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 154 (4), August, 2008)
"In this book the authors present a complete proof of the Langlands conjecture for GL (2) over a non-archimedean local field, which uses local methods and is accessible to students. … The book is very well written and easy to read." (J. G. M. Mars, Zentralblatt MATH, Vol. 1100 (2), 2007)
"The book under review gives a complete and self-contained insight into the theory of representations of G. … We highly recommend this book to Ph.D. students as well as to specialists. The book contains a huge amount of information, definition and facts … . The book has a Bibliography containing 91 references … ." (Alexandru Ioan Badulescu, Mathematical Reviews, Issue 2007 m)
“The aim of this monograph is to present a complete and self-contained proof of the Langlands conjecture for GL(2) over a non-archimedean local field. … This volume presents a large amount of difficult material in a clear and readable manner. It can be recommended to anyone interested in representations of linear algebraic groups.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 154 (4), August, 2008)
Textul de pe ultima copertă
If F is a non-Archimedean local field, local class field theory can be viewed as giving a canonical bijection between the characters of the multiplicative group GL(1,F) of F and the characters of the Weil group of F. If n is a positive integer, the n-dimensional analogue of a character of the multiplicative group of F is an irreducible smooth representation of the general linear group GL(n,F). The local Langlands Conjecture for GL(n) postulates the existence of a canonical bijection between such objects and n-dimensional representations of the Weil group, generalizing class field theory.
This conjecture has now been proved for all F and n, but the arguments are long and rely on many deep ideas and techniques. This book gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groupsand the structure theory of local fields. It uses only local methods, with no appeal to harmonic analysis on adele groups.
This conjecture has now been proved for all F and n, but the arguments are long and rely on many deep ideas and techniques. This book gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groupsand the structure theory of local fields. It uses only local methods, with no appeal to harmonic analysis on adele groups.
Caracteristici
Contributes an unprededented text to the so-called "Langlands theory" An ambitious research program of already 40 years Masterly exposition by authors who have contributed significantly to the Langlands program Includes supplementary material: sn.pub/extras