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.

To appear in Comptes Rendus Mathematique

References in corpus (2)

• On the non-triviality of the $p$-adic Abel-Jacobi image of generalised Heegner cycles modulo $p$, II: Shimura curves
• Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms -- Part II