A result is established about the non-generic cohomology of certain compact unitary Shimura varieties for good p, extending Boyer's work via a different approach in the Fargues-Scholze context.
Towards a theory of local Shimura varieties
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abstract
This is a survey article that advertizes the idea that there should exist a theory of p-adic local analogues of Shimura varieties. Prime examples are the towers of rigid-analytic spaces defined by Rapoport-Zink spaces, and we also review their theory in the light of this idea. We also discuss conjectures on the $\ell$-adic cohomology of local Shimura varieties.
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On the non-generic part of cohomology of compact unitary Shimura varieties of signature $(1,n)$
A result is established about the non-generic cohomology of certain compact unitary Shimura varieties for good p, extending Boyer's work via a different approach in the Fargues-Scholze context.