On the generic part of the cohomology of compact unitary Shimura varieties

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.

Authors

Ana Caraiani

Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

Peter Scholze

Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany