Geodesic
Théorie des nombres
The vanishing of anticyclotomic μ-invariants for non-ordinary modular forms
Hatley, Jeffrey1   ; Lei, Antonio2 
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
Comptes Rendus. Mathématique, Tome 361 (2023) no. G1, pp. 65-72

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Let K be an imaginary quadratic field where p splits. We study signed Selmer groups for non-ordinary modular forms over the anticyclotomic ℤ 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

Hatley, Jeffrey 1 ; Lei, Antonio 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {The vanishing of anticyclotomic $\mu $-invariants for non-ordinary modular forms},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {65--72},
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Hatley, Jeffrey; Lei, Antonio. The vanishing of anticyclotomic $\mu $-invariants for non-ordinary modular forms. Comptes Rendus. Mathématique, Tome 361 (2023) no. G1, pp. 65-72. doi: 10.5802/crmath.389

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