Fitting ideals in two-variable equivariant Iwasawa theory and an application

TL;DR

This paper explores the structure of Iwasawa modules in two-variable equivariant Iwasawa theory for imaginary quadratic fields, linking Fitting ideals to p-adic L-functions and applying results to elliptic curve Selmer groups.

Contribution

It introduces a new description of Fitting ideals of Iwasawa modules in the two-variable setting and applies this to the study of Selmer groups of CM elliptic curves.

Findings

Fitting ideals are expressed via p-adic L-functions.

Results connect Iwasawa modules to elliptic curve Selmer groups.

Provides new tools for understanding equivariant Iwasawa theory.

Abstract

We study equivariant Iwasawa theory for two-variable abelian extensions of an imaginary quadratic field. One of the main goals of this paper is to describe the Fitting ideals of Iwasawa modules using $p$-adic $L$-functions. We also provide an application to Selmer groups of elliptic curves with complex multiplication.