Comptes Rendus
Number theory
The vanishing of anticyclotomic μ-invariants for non-ordinary modular forms
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 65-72.

Let K be an imaginary quadratic field where p splits. We study signed Selmer groups for non-ordinary modular forms over the anticyclotomic p -extension of K, showing that one inclusion of an Iwasawa main conjecture involving the p-adic L-function of Bertolini–Darmon–Prasanna implies that their μ-invariants vanish. This gives an alternative method to reprove a recent result of Matar on the vanishing of the μ-invariants of plus and minus signed Selmer groups for elliptic curves.

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DOI: 10.5802/crmath.389
Classification: 11R23, 11F11, 11R20

Jeffrey Hatley 1; Antonio Lei 2

1 Department of Mathematics, Union College, Bailey Hall 202, Schenectady, NY 12308, USA
2 Department of Mathematics and Statistics, University of Ottawa, 150 Louis-Pasteur Pvt, Ottawa, ON, Canada K1N 6N5
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Jeffrey Hatley; Antonio Lei. The vanishing of anticyclotomic $\mu $-invariants for non-ordinary modular forms. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 65-72. doi : 10.5802/crmath.389. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.389/

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