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November 2017 On the generic part of the cohomology of compact unitary Shimura varieties
Ana Caraiani, Peter Scholze
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Ann. of Math. (2) 186(3): 649-766 (November 2017). DOI: 10.4007/annals.2017.186.3.1

Abstract

The goal of this paper is to show that the cohomology of compact unitary Shimura varieties is concentrated in the middle degree and torsion-free, after localizing at a maximal ideal of the Hecke algebra satisfying a suitable genericity assumption. Along the way, we establish various foundational results on the geometry of the Hodge-Tate period map. In particular, we compare the fibres of the Hodge-Tate period map with Igusa varieties.

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Ana Caraiani. Peter Scholze. "On the generic part of the cohomology of compact unitary Shimura varieties." Ann. of Math. (2) 186 (3) 649 - 766, November 2017. https://doi.org/10.4007/annals.2017.186.3.1

Information

Published: November 2017
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2017.186.3.1

Subjects:
Primary: 11F75 , 11G18

Keywords: Automorphic representations , Galois representations , Shimura varieties , torsion classes

Rights: Copyright © 2017 Department of Mathematics, Princeton University

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Vol.186 • No. 3 • November 2017
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