2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves I
Number Theory
2026-03-02 v4 Algebraic Geometry
Abstract
This paper introduces explicit Galois cohomological methods for determining the ranks of Bloch--Kato Selmer groups associated to the Tate twists of the 2-adic second \'etale cohomology of the Jacobian of a hyperelliptic curve with a rational Weierstrass point. In particular, this can give a method to determine the rational points on such curves via the Chabauty--Coleman--Kim method. This is applied to answer a question of Bugeaud, Mignotte, Siksek, Stoll and Tengely.
Keywords
Cite
@article{arxiv.2312.04996,
title = {2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves I},
author = {Netan Dogra},
journal= {arXiv preprint arXiv:2312.04996},
year = {2026}
}
Comments
Sections 7 and 8 in the previous version moved to a separate document. 34 pages, comments welcome