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Base Change For The Iwahori Hecke Algebra Of Gl2
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Book Synopsis Deformation Theory and Local-Global Compatibility of Langlands Correspondences by : Martin Luu
Download or read book Deformation Theory and Local-Global Compatibility of Langlands Correspondences written by Martin Luu and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The deformation theory of automorphic representations is used to study local properties of Galois representations associated to automorphic representations of general linear groups and symplectic groups. In some cases this allows to identify the local Galois representations with representations predicted by a local Langlands correspondence.
Book Synopsis Arithmetic and Geometry by : Luis Dieulefait
Download or read book Arithmetic and Geometry written by Luis Dieulefait and published by Cambridge University Press. This book was released on 2015-10-08 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on Serre's conjecture and on rational points on algebraic varieties. The resulting proceedings volume provides a modern overview of the subject for graduate students in arithmetic geometry and Diophantine geometry. It is also essential reading for any researcher wishing to keep abreast of the latest developments in the field. Highlights include Tim Browning's survey on applications of the circle method to rational points on algebraic varieties and Per Salberger's chapter on rational points on cubic hypersurfaces.
Book Synopsis Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis by : Gérard Laumon
Download or read book Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis written by Gérard Laumon and published by Cambridge University Press. This book was released on 1996 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1995, Cohomology of Drinfeld Modular Varieties aimed to provide an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands correspondence is a conjectured link between automorphic forms and Galois representations over a global field. By analogy with the number-theoretic case, one expects to establish the conjecture for function fields by studying the cohomology of Drinfeld modular varieties, which has been done by Drinfeld himself for the rank two case. The present volume is devoted to the geometry of these varieties, and to the local harmonic analysis needed to compute their cohomology. Though the author considers only the simpler case of function rather than number fields, many important features of the number field case can be illustrated.
Book Synopsis Derived Langlands: Monomial Resolutions Of Admissible Representations by : Victor P Snaith
Download or read book Derived Langlands: Monomial Resolutions Of Admissible Representations written by Victor P Snaith and published by World Scientific. This book was released on 2018-12-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Langlands Programme is one of the most important areas in modern pure mathematics. The importance of this volume lies in its potential to recast many aspects of the programme in an entirely new context. For example, the morphisms in the monomial category of a locally p-adic Lie group have a distributional description, due to Bruhat in his thesis. Admissible representations in the programme are often treated via convolution algebras of distributions and representations of Hecke algebras. The monomial embedding, introduced in this book, elegantly fits together these two uses of distribution theory. The author follows up this application by giving the monomial category treatment of the Bernstein Centre, classified by Deligne-Bernstein-Zelevinsky.This book gives a new categorical setting in which to approach well-known topics. Therefore, the context used to explain examples is often the more generally accessible case of representations of finite general linear groups. For example, Galois base-change and epsilon factors for locally p-adic Lie groups are illustrated by the analogous Shintani descent and Kondo-Gauss sums, respectively. General linear groups of local fields are emphasized. However, since the philosophy of this book is essentially that of homotopy theory and algebraic topology, it includes a short appendix showing how the buildings of Bruhat-Tits, sufficient for the general linear group, may be generalised to the tom Dieck spaces (now known as the Baum-Connes spaces) when G is a locally p-adic Lie group.The purpose of this monograph is to describe a functorial embedding of the category of admissible k-representations of a locally profinite topological group G into the derived category of the additive category of the admissible k-monomial module category. Experts in the Langlands Programme may be interested to learn that when G is a locally p-adic Lie group, the monomial category is closely related to the category of topological modules over a sort of enlarged Hecke algebra with generators corresponding to characters on compact open modulo the centre subgroups of G. Having set up this functorial embedding, how the ingredients of the celebrated Langlands Programme adapt to the context of the derived monomial module category is examined. These include automorphic representations, epsilon factors and L-functions, modular forms, Weil-Deligne representations, Galois base change and Hecke operators.
Download or read book Mathematical Reviews written by and published by . This book was released on 2001 with total page 902 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Ian Grant Macdonald Publisher :Madras : Ramanujan Institute for Advanced Study in Mathematics, University of Madras ISBN 13 : Total Pages :106 pages Book Rating :4.:/5 (3 download)
Book Synopsis Spherical Functions on a Group of P-adic Type by : Ian Grant Macdonald
Download or read book Spherical Functions on a Group of P-adic Type written by Ian Grant Macdonald and published by Madras : Ramanujan Institute for Advanced Study in Mathematics, University of Madras. This book was released on 1971 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Base Change for GL(2) by : Robert P. Langlands
Download or read book Base Change for GL(2) written by Robert P. Langlands and published by Princeton University Press. This book was released on 1980-07-21 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: R. Langlands shows, in analogy with Artin's original treatment of one-dimensional p, that at least for tetrahedral p, L(s, p) is equal to the L-function L(s, π) attached to a cuspdidal automorphic representation of the group GL(2, /A), /A being the adéle ring of the field, and L(s, π), whose definition is ultimately due to Hecke, is known to be entire. The main result, from which the existence of π follows, is that it is always possible to transfer automorphic representations of GL(2) over one number field to representations over a cyclic extension of the field. The tools he employs here are the trace formula and harmonic analysis on the group GL(2) over a local field.
Download or read book Mikio Sato written by Masaki Kashiwara and published by American Mathematical Society(RI). This book was released on 1998 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Asian Journal of Mathematics by :
Download or read book The Asian Journal of Mathematics written by and published by . This book was released on 1998 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Langlands Correspondence for Loop Groups by : Edward Frenkel
Download or read book Langlands Correspondence for Loop Groups written by Edward Frenkel and published by Cambridge University Press. This book was released on 2007-06-28 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
Book Synopsis Problems on Mapping Class Groups and Related Topics by : Benson Farb
Download or read book Problems on Mapping Class Groups and Related Topics written by Benson Farb and published by American Mathematical Soc.. This book was released on 2006-09-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Book Synopsis Memoirs of the College of Science and Engineering, Waseda University by :
Download or read book Memoirs of the College of Science and Engineering, Waseda University written by and published by . This book was released on 1992 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Memoirs of the School of Science and Engineering, Waseda University by : Waseda Daigaku. Rikō Gakubu
Download or read book Memoirs of the School of Science and Engineering, Waseda University written by Waseda Daigaku. Rikō Gakubu and published by . This book was released on 1995 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hilbert Modular Forms and Iwasawa Theory by : Haruzo Hida
Download or read book Hilbert Modular Forms and Iwasawa Theory written by Haruzo Hida and published by Oxford University Press. This book was released on 2006-06-15 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describing the applications found for the Wiles and Taylor technique, this book generalizes the deformation theoretic techniques of Wiles-Taylor to Hilbert modular forms (following Fujiwara's treatment), and also discusses applications found by the author.
Book Synopsis Towards a Modulo $p$ Langlands Correspondence for GL$_2$ by : Christophe Breuil
Download or read book Towards a Modulo $p$ Langlands Correspondence for GL$_2$ written by Christophe Breuil and published by American Mathematical Soc.. This book was released on 2012-02-22 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct new families of smooth admissible $\overline{\mathbb{F}}_p$-representations of $\mathrm{GL}_2(F)$, where $F$ is a finite extension of $\mathbb{Q}_p$. When $F$ is unramified, these representations have the $\mathrm{GL}_2({\mathcal O}_F)$-socle predicted by the recent generalizations of Serre's modularity conjecture. The authors' motivation is a hypothetical mod $p$ Langlands correspondence.
Download or read book 早稻田大學理工學部紀要 written by and published by . This book was released on 1995 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Eisenstein Series and Automorphic Representations by : Philipp Fleig
Download or read book Eisenstein Series and Automorphic Representations written by Philipp Fleig and published by Cambridge Studies in Advanced. This book was released on 2018-07-05 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
