Anticyclotomic Euler Systems for CM fields

TL;DR

This paper constructs an anticyclotomic Euler system for CM fields under certain conditions and proves one divisibility in the anticyclotomic Iwasawa main conjecture when p is inverted.

Contribution

It introduces a new method to construct anticyclotomic Euler systems for CM fields and proves a key divisibility in the Iwasawa main conjecture.

Findings

Constructed an anticyclotomic Euler system for CM fields.

Proved one divisibility in the anticyclotomic Iwasawa main conjecture.

Applied Urban's method and previous results to achieve these results.

Abstract

Let $K/F$ be a CM extension satisfying the ordinary assumption for an odd prime $p$ and let $\psi$ be a finite order anticyclotomic Hecke character of $K$. When $K$ has a place above $p$ of degree one, we apply Urban's method and the results from our previous work to construct an anticyclotomic Euler system for $\psi$ under minor assumptions and prove one side o the divisibility of the anticyclotomic Iwasawa main conjecture for $\psi$ when $p$ is inverted.