Effective Chabauty for symmetric powers of curves
Name
890211552-MIT.pdf
Description
Full printable version
Size
2.86 MB
Format
Adobe PDF
Checksum (MD5)
3f99b52e08ae20d8cccf5dc397100283
Author(s)
Park, Jennifer Mun Young
Advisor(s)
Bjorn Poonen.
Date Issued
2014
Publisher
Massachusetts Institute of Technology
Abstract
Faltings' theorem states that curves of genus g > 2 have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound on the upper bound on the number of rational points, XI, [paragraph]2, but this bound is too large to be used in any reasonable sense. In 1985, Coleman showed that Chabauty's method, which works when the Mordell-Weil rank of the Jacobian of the curve is smaller than g, can be used to give a good effective bound on the number of rational points of curves of genus g > 1. We draw ideas from nonarchimedean geometry to show that we can also give an effective bound on the number of rational points outside of the special set of Symd X, where X is a curve of genus g > d, when the Mordell-Weil rank of the Jacobian of the curve is at most g > d.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 75-76).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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