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Published December 2018 | Accepted Version
Journal Article Open

Harris-Viehmann conjecture for Hodge-Newton reducible Rapoport-Zink spaces

Hong, Serin

Abstract

Rapoport–Zink spaces, or more generally local Shimura varieties, are expected to provide geometric realization of the local Langlands correspondence via their l‐adic cohomology. Along this line is a conjecture by Harris and Viehmann, which roughly says that when the underlying local Shimura datum is not basic, the l‐adic cohomology of the local Shimura variety is parabolically induced. We verify this conjecture for Rapoport–Zink spaces which are Hodge type and Hodge–Newton reducible. The main strategy is to embed such a Rapoport–Zink space into an appropriate space of EL type, for which the conjecture is already known to hold by the work of Mantovan.

Additional Information

© 2018 London Mathematical Society. Received 1 June 2017; published online 24 July 2018. I would like to express my deepest gratitude to Elena Mantovan. This study would have never been possible without her previous work for EL/PEL cases and her numerous helpful suggestions.

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Created:
August 19, 2023
Modified:
October 19, 2023