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arxiv: 1401.2849 · v2 · pith:EMLDU35Mnew · submitted 2014-01-13 · 🧮 math.AG · math.NT· math.RT

Towards a theory of local Shimura varieties

Michael Rapoport , Eva Viehmann This is my paper
classification 🧮 math.AG math.NTmath.RT
keywords localshimuratheoryvarietiesideaspacesadicadvertizes
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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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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On the non-generic part of cohomology of compact unitary Shimura varieties of signature $(1,n)$

    math.NT 2025-11 unverdicted novelty 5.0

    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.