Speaker: Shaunak Deo, IISc Bangalore

Time & Date: 4 pm, Friday, 29 July 2022

Venue: Ramanujan Hall

Title: The Eisenstein ideal of weight $k$ and ranks of Hecke algebras

Abstract: Let $p$ and $\ell$ be primes such that $p > 3$ and $p \mid
\ell-1$ and $k$ be an even integer. Using deformation theory of Galois
representations, we will give a necessary and sufficient condition for the
$Z_p$-rank of the completion of the Hecke algebra acting on the space of
cuspidal modular forms of weight $k$ and level $\Gamma_0(\ell)$ at the
maximal Eisenstein ideal containing $p$ to be greater than $1$ in terms of
vanishing of the cup products of certain global Galois cohomology classes.