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Title:Special fibers of Shimura varieties in the Torelli locus
Author(s):Donepudi, Ravi Kiran
Director of Research:Allen, Patrick
Doctoral Committee Chair(s):Ahlgren, Scott
Doctoral Committee Member(s):Zaharescu, Alexandru; Duursma, Iwan
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:2021-04-23
Type:Thesis
URI:http://hdl.handle.net/2142/110498
Rights Information:Copyright 2021 Ravi Kiran Donepudi
Date Available in IDEALS:2021-09-17
Date Deposited:2021-05


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