University of Illinois Urbana-Champaign

Special fibers of Shimura varieties in the Torelli locus

Donepudi, Ravi Kiran

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https://hdl.handle.net/2142/110498

Description

Title
Special fibers of Shimura varieties in the Torelli locus
Author(s)
Donepudi, Ravi Kiran
Issue Date
2021-04-23
Director of Research (if dissertation) or Advisor (if thesis)
Allen, Patrick
Doctoral Committee Chair(s)
Ahlgren, Scott
Committee Member(s)
  • Zaharescu, Alexandru
  • Duursma, Iwan
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Abelian Varieties
  • Shimura Varieties
  • Torelli Locus
  • Newton Polygon
  • Ekedahl-Oort type
Abstract
In this dissertation, we study the special fibers of thirteen Shimura varieties with an irreducible component containing a dense subset of Jacobians. The relevant Jacobians arise from branched non-abelian Galois covers of the projective line. Using the action of the Galois group of the cover, we are able to determine the position of the special fibers of these Shimura varieties inside the Siegel modular variety with respect to the Newton and Ekedahl-Oort stratifications in positive characteristic.
Graduation Semester
2021-05
Type of Resource
Thesis
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http://hdl.handle.net/2142/110498
Copyright and License Information
Copyright 2021 Ravi Kiran Donepudi

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