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arXiv · 2312.04996

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

Netan Dogra
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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.

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Netan Dogra. 2023-12-08. 2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves I. https://arxiv.org/abs/2312.04996

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