Shimura varieties / edited by Thomas Haines, Michael Harris.

Format:

Book

Contributor:

Haines, Thomas J., editor.

Harris, Michael, 1954- editor.

Series:

London Mathematical Society lecture note series ; 457.

London Mathematical Society lecture note series ; 457

Language:

English

French

Subjects (All):

Shimura varieties.

Automorphic forms.

Physical Description:

333 pages : illustrations ; 23 cm.

Continues:

On the stabilization of the trace formula. Somerville, Mass : International Press, 2011

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020.

Language Note:

Text in English with one contribution in French.

Summary:

"This is the second volume of a projected series of two or three collections of mainly expository articles on the arithmetic theory of automorphic forms. The books are intended primarily for two groups of readers. The first group is interested in the structure of automorphic forms on reductive groups over number fields, and specifically in qualitative information about the multiplicities of automorphic representations. The second group is interested in the problem of classifying I-adic representations of Galois groups of number fields. Langlands' conjectures elaborate on the notion that these two problems overlap to a considerable degree. The goal of this series of books is to gather into one place much of the evidence that this is the case, and to present it clearly and succinctly enough so that both groups of readers are not only convinced by the evidence but can pass with minimal effort between the two points of view. More than a decade's worth of progress toward the stabilization of the Arthur-Selberg trace formula, culminating in Ngo Bau Chau's proof of the Fundamental Lemma, has made this series timely"-- Provided by publisher.

Contents:

Introduction to Volume II / T. J. Haines and M. Harris

Lectures on Shimura varieties / A. Genestier and B.C. Ngô

Unitary Shimura varieties / Marc-Hubert Nicole

Integral models of Shimura varieties of PEL type / Sandra Rozensztajn

Introduction to the Langlands-Kottwitz method / Yihang Zhu

Integral Canonical Models of Shimura varieties : an update / Mark Kisin

The Newton stratification / Elena Mantovan

On the geometry of the Newton stratification / Eva Viehmann

Construction of automorphic Galois representations : the self-dual case / Sug Woo Shin

The local Langlands correspondence for GLn over p-adic fields, and the cohomology of compact unitary Shimura varieties / Peter Scholze

Une application des variétés de Hecke des groupes unitaires / Gaëtan Chenevier

A patching lemma / Claus M. Sorensen

On subquotients of the étale cohomology of Shimura varieties / Christian Johansson and Jack A. Thorne.

Notes:

"This volume forms the sequel to On the stabilization of the trace formula published by International Press of Boston, Inc., 2011."

Includes bibliographical references.

Other Format:

Online version: Shimura varieties.

ISBN:

9781108704861

1108704867

OCLC:

1120186583