Shimura Varieties

Thomas Haines, Michael Harris

• Publisher: Cambridge University Press
• Year: 2020
• Print ISBN: 9781108704861
• eBook ISBN: 9781108620383
• Topic: Mathematics
• Subtopic: Number Theory
• Index: Mathematics

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.

Table of contents

• Cover
• Series information
• Title page
• Copyright information
• Contents
• Introduction to Volume II
• Lectures on Shimura varieties
• Unitary Shimura varieties
• Integral models of Shimura varieties of PEL type
• Introduction to the Langlands–Kottwitz method
• Integral Canonical Models of Shimura varieties: an update
• The Newton stratification
• On the geometry of the Newton stratification
• Construction of automorphic Galois representations: the self-dual case
• The local Langlands correspondence for GL[sub(n)] over p-adic fields, and the cohomology of compact unitary Shimura varieties
• Une application des variétés de Hecke des groupes unitaires
• A Patching Lemma
• On subquotients of the étale cohomology of Shimura varieties