Colloquium abstracts

Jacques Tilouine
Universite Sorbonne Paris Nord
January 21, 2021

Derived deformation rings and adjoint Selmer groups for GL_N over a CM field:  Given a cuspidal automorphic representation $pi$ on $GL_N(F)$, for a CM field $F$ with Galois representation $rho_pi$, say, ordinary at $p$, we define and study, under certain assumptions, a homomorphism from the fundamental group of the deformation of $rho_pi$ to its dual adjoint Selmer group.It has been defined and studied earlier by Galatius and Venkatesh under stricter assumptions. Our more general setting shows a new feature of this homomorphism, namely the relation between the derived deformation ring of $rho_pi$ and the Bloch-Kato conjecture for the adjoint representation of $rho_pi$. We treat as well the situation of Hida families. This is a joint work with E. Urban.