Effective Chabauty for symmetric powers of curves
Author(s)Park, Jennifer Mun Young
Massachusetts Institute of Technology. Department of Mathematics.
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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.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.Cataloged from PDF version of thesis.Includes bibliographical references (pages 75-76).
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology