The vanishing of anticyclotomic $\mu$-invariants for non-ordinary modular forms

TL;DR

This paper proves that the $$-invariants of signed Selmer groups for non-ordinary modular forms over anticyclotomic extensions of imaginary quadratic fields are zero, extending previous results for elliptic curves.

Contribution

It generalizes the vanishing of $$-invariants to non-ordinary modular forms and provides a new proof of related recent results.

Findings

$$-invariants of signed Selmer groups vanish

Extends results from elliptic curves to modular forms

Provides a new proof technique for $$-invariant vanishing

Abstract

Let $K$ be an imaginary quadratic field where $p$ splits. We study signed Selmer groups for non-ordinary modular forms over the anticyclotomic $\mathbf{Z}_p$-extension of $K$, showing that their $\mu$-invariants vanish. This generalizes and gives a new proof of a recent result of Matar on the vanishing of the $\mu$-invariants of plus and minus signed Selmer groups for elliptic curves.