Euler systems and the BSD conjecture for abelian surfaces

Abstract: Euler systems are one of the most powerful tools for proving cases of the Bloch--Kato conjecture, and other related problems such as the Birch and Swinnerton-Dyer conjecture. I will recall a series of recent works (variously joint with Loeffler, Pilloni, Skinner) giving rise to an Euler system in the cohomology of Shimura varieties for GSp(4), and an explicit reciprocity law relating this to values of L-functions. I will then explain work in progress with Loeffler, in which we use this Euler system to prove new cases of the BSD conjecture for modular abelian surfaces over Q, and modular elliptic curves over imaginary quadratic fields.

number theory

Audience: researchers in the topic

London number theory seminar

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