University of Cambridge > Talks.cam > Number Theory Seminar > Explicit Chabauty over Number Fields

Explicit Chabauty over Number Fields

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Tom Fisher.

Let C be a curve of genus at least 2 over a number field K of degree d. Let J be the Jacobian of C and r the rank of the Mordell-Weil group J(K). Chabauty is a practical method for explicitly computing C(K) provided r <= g – 1. In unpublished work, Wetherell suggested that Chabauty’s method should still be applicable provided the weaker bound r <= d (g – 1) is satisfied. We give details of this and use it to solve the Diophantine equation x2 + y3 = z10 by reducing the problem to determining the K-rational points on several genus 2 curves over K = Q(cube root of 2).

This talk is part of the Number Theory Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2024 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity