On the Iwasawa Main Conjecture for generalized Heegner classes in a quaternionic setting
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929268148142080 |
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| author | Pati, Maria Rosaria |
| author_facet | Pati, Maria Rosaria |
| contents | We prove one divisibility relation of the anticyclotomic Iwasawa Main Conjecture for a higher weight ordinary modular form $f$ and an imaginary quadratic field satisfying a "relaxed" Heegner hypothesis. Let $Λ$ be the anticyclotomic Iwasawa algebra. Following the approach of Howard and Longo--Vigni, we construct the $Λ$-adic Kolyvagin system of generalized Heegner classes coming from Heegner points on a suitable Shimura curve. As its application, we also prove one divisibility relation in the Iwasawa-Greenberg main conjecture for the $p$-adic $L$-function defined by Magrone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08934 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Iwasawa Main Conjecture for generalized Heegner classes in a quaternionic setting Pati, Maria Rosaria Number Theory 11R23, 11F11 We prove one divisibility relation of the anticyclotomic Iwasawa Main Conjecture for a higher weight ordinary modular form $f$ and an imaginary quadratic field satisfying a "relaxed" Heegner hypothesis. Let $Λ$ be the anticyclotomic Iwasawa algebra. Following the approach of Howard and Longo--Vigni, we construct the $Λ$-adic Kolyvagin system of generalized Heegner classes coming from Heegner points on a suitable Shimura curve. As its application, we also prove one divisibility relation in the Iwasawa-Greenberg main conjecture for the $p$-adic $L$-function defined by Magrone. |
| title | On the Iwasawa Main Conjecture for generalized Heegner classes in a quaternionic setting |
| topic | Number Theory 11R23, 11F11 |
| url | https://arxiv.org/abs/2304.08934 |