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

2023/12/08 by Dogra, Netan · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2312.04996

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.

Cited by

• Determining the rational points on a curve of genus 2 and Mordell-Weil rank 1
• Generalised height pairings and the Albanese kernel

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