The vanishing of anticyclotomic $\mu $-invariants for non-ordinary modular forms
Let $K$ be an imaginary quadratic field where $p$ splits. We study signed Selmer groups for non-ordinary modular forms over the anticyclotomic $\mathbb{Z}_p$-extension of $K$, showing that one inclusion of an Iwasawa main conjecture involving the $p$-adic $L$-function of Bertolini–Darmon–Prasanna im...
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Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.389/ |
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| author | Hatley, Jeffrey Lei, Antonio |
| author_facet | Hatley, Jeffrey Lei, Antonio |
| author_sort | Hatley, Jeffrey |
| collection | DOAJ |
| description | Let $K$ be an imaginary quadratic field where $p$ splits. We study signed Selmer groups for non-ordinary modular forms over the anticyclotomic $\mathbb{Z}_p$-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 $\mu $-invariants vanish. This gives an alternative method to reprove a recent result of Matar on the vanishing of the $\mu $-invariants of plus and minus signed Selmer groups for elliptic curves. |
| format | Article |
| id | doaj-art-b2d7068514be4492a12bacd03eb68086 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-b2d7068514be4492a12bacd03eb680862025-02-07T11:06:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-01-01361G1657210.5802/crmath.38910.5802/crmath.389The vanishing of anticyclotomic $\mu $-invariants for non-ordinary modular formsHatley, Jeffrey0https://orcid.org/0000-0002-6883-1316Lei, Antonio1https://orcid.org/0000-0001-9453-3112Department of Mathematics, Union College, Bailey Hall 202, Schenectady, NY 12308, USADepartment of Mathematics and Statistics, University of Ottawa, 150 Louis-Pasteur Pvt, Ottawa, ON, Canada K1N 6N5Let $K$ be an imaginary quadratic field where $p$ splits. We study signed Selmer groups for non-ordinary modular forms over the anticyclotomic $\mathbb{Z}_p$-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 $\mu $-invariants vanish. This gives an alternative method to reprove a recent result of Matar on the vanishing of the $\mu $-invariants of plus and minus signed Selmer groups for elliptic curves.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.389/ |
| spellingShingle | Hatley, Jeffrey Lei, Antonio The vanishing of anticyclotomic $\mu $-invariants for non-ordinary modular forms Comptes Rendus. Mathématique |
| title | The vanishing of anticyclotomic $\mu $-invariants for non-ordinary modular forms |
| title_full | The vanishing of anticyclotomic $\mu $-invariants for non-ordinary modular forms |
| title_fullStr | The vanishing of anticyclotomic $\mu $-invariants for non-ordinary modular forms |
| title_full_unstemmed | The vanishing of anticyclotomic $\mu $-invariants for non-ordinary modular forms |
| title_short | The vanishing of anticyclotomic $\mu $-invariants for non-ordinary modular forms |
| title_sort | vanishing of anticyclotomic mu invariants for non ordinary modular forms |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.389/ |
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