Dissertation/Thesis Abstract

Towards an unconditional proof of the André-Oort Conjecture and surrounding problems
by Tsimerman, Jacob, Ph.D., Princeton University, 2011, 104; 3463338
Abstract (Summary)

We take steps towards carrying out Pila's strategy for proving the André-Oort conjecture unconditionally. Specifically, we prove lower bounds for galois orbits of special points in the [special characters omitted] for g ≤ 6. We then (joint with J.Pila) carry out the rest of Pila's program for [special characters omitted] and obtain an unconditional proof of André-Oort in this case. We also settle a conjecture of Nicholas Katz and Frans Oort by proving that for every g ≥ 4, there exists an abelian variety of dimension g over [special characters omitted] that's not isogenous to any Jacobian.

Indexing (document details)
Advisor: Sarnak, Peter
School: Princeton University
School Location: United States -- New Jersey
Source: DAI-B 72/10, Dissertation Abstracts International
Subjects: Applied Mathematics, Mathematics
Keywords: Abelian variety, Andre-Oort conjecture, Galois orbits, Lower bounds, Special points
Publication Number: 3463338
ISBN: 9781124735283
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