On characteristic power series of dual signed Selmer groups

Abstract: In joint work with Jishnu Ray, we relate the cardinality of the p-primary part of the Bloch-Kato Selmer group over Q attached to a modular form at a non-ordinary prime p to the constant term of the characteristic power series of the signed Selmer groups over the cyclotomic Zp-extension of Q. This generalizes a result of Vigni and Longo in the ordinary case. In the case of elliptic curves, such results follow from earlier works by Greenberg, Kim, the second author, and Ahmed–Lim, covering both the ordinary and most of the supersingular case.

algebraic geometrynumber theory

Audience: researchers in the topic

UCSB Seminar on Geometry and Arithmetic