Independence of rational points on twists of a given curve
Number Theory
2007-05-23 v1
Abstract
In this paper, we study bounds for the number of rational points on twists C' of a fixed curve C over a number field K, under the condition that the group of K-rational points on the Jacobian J' of C' has rank smaller than the genus of C'. The main result is that with some explicitly given finitely many possible exceptions, we have a bound of the form 2r + c, where r is the rank of J'(K) and c is a constant depending on C. For the proof, we use a refinement of the method of Chabauty-Coleman; the main new ingredient is to use it for an extension field of K_v, where v is a place of bad reduction for C'.
Keywords
Cite
@article{arxiv.math/0603557,
title = {Independence of rational points on twists of a given curve},
author = {Michael Stoll},
journal= {arXiv preprint arXiv:math/0603557},
year = {2007}
}
Comments
16 pages; to appear in Compositio Math (in a slightly different version)