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

2015/11/08 by Caraiani, Ana, Scholze, Peter
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1511.02418

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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