Iwasawa theory over imaginary quadratic fields for inert primes

Abstract: Let $p$ be a fixed odd prime and $K$ an imaginary quadratic field where $p$ is inert. Let $f$ be an elliptic modular form with good ordinary reduction at $p$. We discuss how the cyclotomic Iwasawa theory of the Rankin-Selberg product of $f$ and a $p$-non-ordinary CM form allows us to study the Iwasawa theory of $f$ over the $\mathbf{Z}_p^2$-extension of $K$. We make use of the plus and minus theory of Kobayashi and Pollack as well as Euler systems built out of Beilinson--Flach elements. This is joint work with Kazim Buyukboduk.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Columbia Automorphic Forms and Arithmetic Seminar