Read more
A concise and comprehensive introduction to trace formula methods in the study of Shimura varieties and associated Galois representations.
List of 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.
About the author
Thomas Haines is a Professor of Mathematics at the University of Maryland, College Park. He has authored over thirty research articles, several survey articles on matters related to the Langlands program, and a monograph on commutative algebra. He has been awarded a Sloan Fellowship and a Simons Research Fellowship.Michael Harris is a Professor of Mathematics at Columbia University and the Université Paris Diderot. He is the author or co-author of nearly 90 mathematical books and articles, and he has received a number of prizes, including the Grand Prix Sophie Germain of the Académie des Sciences, and the Clay Research Award, which he shared in 2007 with Richard Taylor.
Summary
The book is designed for graduate students and beginning researchers into the arithmetic theory of automorphic forms, and for all who want to know more about the Langlands program. It forms a sequel to On the Stabilization of the Trace Formula published in 2011.
