• Corpus ID: 25848547

Towards a theory of local Shimura varieties

  title={Towards a theory of local Shimura varieties},
  author={Michael Rapoport and Eva Viehmann},
  journal={arXiv: Algebraic Geometry},
This is a survey article that advertises 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 l-adic cohomology of local Shimura varieties. 
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