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

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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     title = {On the generic part of the cohomology of compact unitary {Shimura} varieties},
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Ana Caraiani; Peter Scholze. On the generic part of the cohomology of compact unitary Shimura varieties. Annals of mathematics, Volume 186 (2017) no. 3, pp. 649-766. doi: 10.4007/annals.2017.186.3.1

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