On adjoint Bloch--Kato Selmer groups for $\mathrm{GSp}_{2g}$

TL;DR

This paper investigates the structure of adjoint Bloch--Kato Selmer groups linked to classical points on the eigenvariety for GSp(2g), using families of Galois representations inspired by Bellaiche and Chenevier.

Contribution

It introduces a new approach to studying Selmer groups via eigenvarieties and Galois representation families for symplectic groups.

Findings

Analysis of Selmer groups in the GSp(2g) context

Development of a family-based method for Selmer group study

Insights into the variation of Selmer groups across eigenvarieties

Abstract

We study the adjoint Bloch--Kato Selmer groups attached to a classical point in the cuspidal eigenvariety associated with $\mathrm{GSp}_{2g}$. Our strategy is based on the study of families of Galois representations on the eigenvariety, which is inspired by the book of J. Bellaiche and G. Chenevier.