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Shimura Varieties

Shimura Varieties

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Part of London Mathematical Society Lecture Note Series

T. J. Haines, M. Harris, A. Genestier, B. C. Ngo, Marc-Hubert Nicole, Sandra Rozensztajn, Yihang Zhu, Mark Kisin, Elena Mantovan, Eva Viehmann, Sug Woo Shin, Peter Scholze, Gaetan Chenevier, Claus M. Sorensen, Christian Johansson, Jack A. Thorne
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  • Publication planned for: February 2020
  • availability: Not yet published - available from February 2020
  • format: Paperback
  • isbn: 9781108704861

Price is not yet set
Paperback

Not yet published - available from February 2020
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About the Authors
  • 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.

    • Systematically develops the Langlands–Kottwitz method for Shimura varieties through the important example of unitary groups
    • Constructs Galois representations attached to automorphic representations of GL(n)
    • Includes several surveys of contemporary developments as well as original research
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    Product details

    • Publication planned for: February 2020
    • format: Paperback
    • isbn: 9781108704861
    • dimensions: 228 x 152 mm
    • availability: Not yet published - available from February 2020
  • Table 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.

  • Editors

    Thomas Haines, University of Maryland, College Park
    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, Columbia University, New York
    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.

    Contributors

    T. J. Haines, M. Harris, A. Genestier, B. C. Ngo, Marc-Hubert Nicole, Sandra Rozensztajn, Yihang Zhu, Mark Kisin, Elena Mantovan, Eva Viehmann, Sug Woo Shin, Peter Scholze, Gaetan Chenevier, Claus M. Sorensen, Christian Johansson, Jack A. Thorne

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