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

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.