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

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.