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

Hatley, Jeffrey; Lei, Antonio

doi:10.5802/crmath.389

Théorie des nombres

The vanishing of anticyclotomic

μ

-invariants for non-ordinary modular forms

Hatley, Jeffrey ¹ ; Lei, Antonio ²

¹Department of Mathematics, Union College, Bailey Hall 202, Schenectady, NY 12308, USA
²Department 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

Résumé

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.

Reçu le : 2021-08-12
Révisé le : 2022-04-28
Accepté le : 2022-06-02
Publié le : 2023-01-12

DOI : 10.5802/crmath.389

Classification : 11R23, 11F11, 11R20

Affiliations des auteurs :

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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