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Full Description
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 T. J. Haines and M. Harris; 1. Lectures on Shimura varieties A. Genestier and B. C. Ngo; 2. Unitary Shimura varieties Marc-Hubert Nicole; 3. Integral models of Shimura varieties of PEL type Sandra Rozensztajn; 4. Introduction to the Langlands-Kottwitz method Yihang Zhu; 5. Integral canonical models of Shimura varieties Mark Kisin; 6. The Newton stratification Elena Mantovan; 7. On the geometry of the Newton stratification Eva Viehmann; 8. Construction of automorphic Galois representations Sug Woo Shin; 9. The local Langlands correspondence for GLn over p-adic fields, and the cohomology of compact unitary Shimura varieties Peter Scholze; 10. Une application des varietes de Hecke des groupes unitaires Gaetan Chenevier; 11. A patching lemma Claus M. Sorensen; 12. On subquotients of the etale cohomology of Shimura varieties Christian Johansson and Jack A. Thorne.
