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On Hodge-Newton Reducible Local Shimura Data of Hodge Type


Hong, Serin (2018) On Hodge-Newton Reducible Local Shimura Data of Hodge Type. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4F4W-Y024.


Rapoport-Zink spaces are formal moduli spaces of p-divisible groups which give rise to local analogues of certain Shimura varieties. In particular, one can construct them from purely group theoretic data called local Shimura data.

The primary purpose of this dissertation is to study Rapoport-Zink spaces whose underlying local Shimura datum is of Hodge type and Hodge-Newton reducible. Our study consists of two main parts: the study of the l-adic cohomology of Rapoport-Zink spaces in relation to the local Langlands correspondence and the study of deformation spaces of p-divisible groups via the local geometry of Rapoport-Zink spaces.

The main result of the first part is a proof of the Harris-Viehmann conjecture in our setting; in particular, we prove that the l-adic cohomology of Rapoport-Zink spaces contains no supercuspidal representations under our assumptions. In the second part, we obtain a generalization of Serre-Tate deformation theory for Shimura varieties of Hodge type.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Shimura varieties, Local Langlands correspondence, Rapoport-Zink spaces
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Scott Russell Johnson Graduate Dissertation Prize in Mathematics, 2018. Apostol Award for Excellence in Teaching in Mathematics, 2016. Scott Russell Johnson Prize for Excellence in Graduate Studies, 2014.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Mantovan, Elena
Thesis Committee:
  • Mantovan, Elena (chair)
  • Ramakrishnan, Dinakar
  • Zhu, Xinwen
  • Amir Khosravi, Zavosh
Defense Date:9 April 2018
Record Number:CaltechTHESIS:05262018-184212374
Persistent URL:
Hong, Serin0000-0002-0410-9041
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10943
Deposited By: Serin Hong
Deposited On:30 May 2018 18:49
Last Modified:04 Oct 2019 00:21

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