


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 $p \mid \ell1$ 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.