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arXiv · 1511.02418

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

Ana Caraiani·Peter Scholze
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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. 2015-11-08. On the generic part of the cohomology of compact unitary Shimura varieties. https://arxiv.org/abs/1511.02418

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