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.
|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|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be