Shimura varieties /
edited by Thomas Haines, Michael Harris.
- Cambridge : Cambridge University Press, 2020.
- 1 online resource (333 pages) : digital, PDF file(s).
- London Mathematical Society lecture note series; 457 .
- London Mathematical Society lecture note series; 457. .
Title from publisher's bibliographic system (viewed on 07 Feb 2020).
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.
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.