Shimura varieties / edited by Thomas Haines, Michael Harris.

Format:

Book

Contributor:

Haines, Thomas, editor.

Harris, Michael, 1954- editor.

Series:

London Mathematical Society lecture note series; 457.

London Mathematical Society lecture note series; 457

Language:

English

Subjects (All):

Shimura varieties.

Automorphic forms.

Physical Description:

1 online resource (333 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2020.

Language Note:

English

Summary:

This is the second volume of a series of mainly expository articles on the arithmetic theory of automorphic forms. It forms a sequel to On the Stabilization of the Trace Formula published in 2011. The books are intended primarily for two groups of readers: those interested in the structure of automorphic forms on reductive groups over number fields, and specifically in qualitative information on multiplicities of automorphic representations; and those interested in the classification of I-adic representations of Galois groups of number fields. Langlands' conjectures elaborate on the notion that these two problems overlap considerably. These volumes present convincing evidence supporting this, clearly and succinctly enough that readers can pass with minimal effort between the two points of view. Over 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, makes this series timely.

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:

Title from publisher's bibliographic system (viewed on 07 Feb 2020).

Includes bibliographical references.

ISBN:

1-108-63206-8

1-108-62038-8

1-108-64971-8