2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves I

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 étale 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.

arXiv commentSections 7 and 8 in the previous version moved to a separate document. 34 pages, comments welcome