Speaker: Chandrashekhar Khare
Affiliation: University of California, Los Angeles
Title of Talk: Towards the $p$-part of the Bloch-Kato conjecture for $L(1,Ad_f)$ at all primes $p$
Date: March 25, 2026
Time: 14:00:00 Hours
Venue: AG-77

Abstract: I will discuss ongoing work with Diamond, Iyengar, and Manning building on our earlier research on the numerical criterion of Wiles. This work has led us to consider local congruence ideals: these are local counterparts of the congruence ideals at newforms of Hecke algebras that have been studied extensively since the 1980s (e.g., in the work of Mazur, Ribet, Hida, and Wiles). These local ideals shed new light on their global counterparts, to which they are related in a way analogous to the relationship between local and global Galois cohomology. Our work provides an approach to the $p$-part of the Bloch-Kato conjecture for $L(1, \text{Ad}_f)$, where $f$ is a newform of level $N$ and weight $k$, for primes $p$ that divide $Nk!$.