Speaker: Arshay Sheth
Affiliation: TIFR, Mumbai
Title of Talk: $p$-adic variation of Euler systems
Date: December 02, 2025
Time: 16:00:00 Hours
Venue: AG-77

Abstract: Euler systems are cohomological tools that play a crucial role in the study of special values of L-functions; for instance, they have been used to prove cases of the Birch--Swinnerton-Dyer conjecture and have recently been used to prove cases of the more general Bloch--Kato conjecture. A fundamental technique in these recent advances is to show that Euler systems vary in p-adic families. In this talk, we will first give a general introduction to the theme of p-adic variation in number theory and introduce the necessary background from the theory of Euler systems; we will then explain the idea and importance of p-adically varying Euler systems, and finally discuss recent results on p-adically varying the Asai--Flach Euler system, which is an Euler system arising from quadratic Hilbert modular eigenforms.