Shimura varieties.

*(English)*Zbl 1435.14004
London Mathematical Society Lecture Note Series 457. Cambridge: Cambridge University Press (ISBN 978-1-108-70486-1/pbk; 978-1-108-64971-1/ebook). iii, 333 p. (2020).

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

The articles of this volume will be reviewed individually.

Indexed articles:

Haines, T. J.; Harris, M., Introduction to Volume II, 1-21 [Zbl 1436.11004]

Genestier, A.; Ngô, B. C., Lectures on Shimura varieties, 22-71 [Zbl 1440.11001]

Nicole, Marc-Hubert, Unitary Shimura varieties, 72-95 [Zbl 1440.14138]

Rozensztajn, Sandra, Integral models of Shimura varieties of PEL type, 96-114 [Zbl 1440.14139]

Zhu, Yihang, Introduction to the Langlands-Kottwitz method, 115-150 [Zbl 1440.14141]

Kisin, Mark, Integral canonical models of Shimura varieties: an update, 151-165 [Zbl 1440.14136]

Mantovan, Elena, The Newton stratification, 166-191 [Zbl 1440.14115]

Viehmann, Eva, On the geometry of the Newton stratification, 192-208 [Zbl 1440.14140]

Shin, Sug Woo, Construction of automorphic Galois representations: the self-dual case, 209-250 [Zbl 1455.11079]

Scholze, Peter, The local Langlands correspondence for GL\(_n\) over \(p\)-adic fields, and the cohomology of compact unitary Shimura varieties, 251-265 [Zbl 1440.11218]

Chenevier, Gaëtan, An application of Hecke varieties from unitary groups, 266-296 [Zbl 07219416]

Sorensen, Claus M., A patching lemma, 297-305 [Zbl 1440.11219]

Johansson, Christian; Thorne, Jack A., On subquotients of the étale cohomology of Shimura varieties, 306-333 [Zbl 07219418]

##### MSC:

14-06 | Proceedings, conferences, collections, etc. pertaining to algebraic geometry |

11-06 | Proceedings, conferences, collections, etc. pertaining to number theory |

14G35 | Modular and Shimura varieties |

11G18 | Arithmetic aspects of modular and Shimura varieties |

00B15 | Collections of articles of miscellaneous specific interest |