Refined effective bounds for Bloch-Kato Selmer groups associated to hyperelliptic curves

2025/02/16 by Berry, Lee · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.11154

Abstract

We develop refined methods to effectively bound the dimension of Bloch-Kato Selmer groups associated to the higher Chow group CH²(J,1), where J is the Jacobian of a hyperelliptic curve X. This extends the recent work of Dogra on explicit 2-descent for these Selmer groups to include cases where X does not have a rational Weierstrass point. Additionally, we develop methods for obtaining sharper dimension bounds under the assumption that X has good ordinary reduction at 2. As a consequence, we establish new criteria for deducing finiteness of the depth 2 Chabauty-Kim set X(ℚ₂)₂, and demonstrate the efficacy of these criteria on curves from the LMFDB.

Cited by

• Generalised height pairings and the Albanese kernel

Related

• 2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves II
• 2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves I
• Bounds on the Chabauty--Kim Locus of Hyperbolic Curves
• 2-Selmer groups of hyperelliptic curves with two marked points
• The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point