Special fibers of Shimura varieties in the Torelli locus

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2021

Author dc:creator

• Donepudi, Ravi Kiran

Contributors dc:contributor

• Allen, Patrick
• Ahlgren, Scott
• Zaharescu, Alexandru
• Duursma, Iwan

• Abelian Varieties
• Shimura Varieties
• Torelli Locus
• Newton Polygon
• Ekedahl-Oort type

Statement dc:rights

• Copyright 2021 Ravi Kiran Donepudi

Language dc:language

en

Handle dc:identifier

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

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F110498