## Effective Chabauty for symmetric powers of curves

##### Author(s)

Park, Jennifer Mun Young
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##### Other Contributors

Massachusetts Institute of Technology. Department of Mathematics.

##### Advisor

Bjorn Poonen.

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Show full item record##### 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).

##### Date issued

2014##### Department

Massachusetts Institute of Technology. Department of Mathematics##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.