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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1778-3569 |