Geodesic
On the generic part of the cohomology of compact unitary Shimura varieties
Ana Caraiani1 ; Peter Scholze2
1 Mathematisches Institut der Universität Bonn, Bonn, Germany
2 Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
Annals of mathematics, Tome 186 (2017) no. 3, pp. 649-766.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2017.186.3.1

Ana Caraiani 1 ; Peter Scholze 2

1 Mathematisches Institut der Universität Bonn, Bonn, Germany
2 Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany 
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Ana Caraiani; Peter Scholze. On the generic part of the cohomology of compact unitary Shimura varieties. Annals of mathematics, Tome 186 (2017) no. 3, pp. 649-766. doi : 10.4007/annals.2017.186.3.1. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.186.3.1/

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