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

Hong, Serin (2018) Harris-Viehmann conjecture for Hodge-Newton reducible Rapoport-Zink spaces. Journal of the London Mathematical Society, 98 (3). pp. 733-752. ISSN 0024-6107. https://resolver.caltech.edu/CaltechAUTHORS:20181220-092840529

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1112/jlms.12160DOIArticle
https://arxiv.org/abs/1612.08475arXivDiscussion Paper
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.
Issue or Number:3
Classification Code:2010 Mathematics Subject Classification: 11G18 (primary), 14G35 (secondary)
Record Number:CaltechAUTHORS:20181220-092840529
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181220-092840529
Official Citation:Hong, S. (2018), Harris–Viehmann conjecture for Hodge–Newton reducible Rapoport–Zink spaces. J. London Math. Soc., 98: 733-752. doi:10.1112/jlms.12160
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91925
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:20 Dec 2018 17:53
Last Modified:03 Oct 2019 20:39

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