Quaternionic Kolyvagin systems and Iwasawa theory for Hida families
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908867589308416 |
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| author | Zerman, Francesco |
| author_facet | Zerman, Francesco |
| contents | We build a modified universal Kolyvagin system for the Galois representation attached to a Hida family of modular forms, starting from the big Heegner point Euler system of Longo--Vigni built in towers of Shimura curves. We generalize the work of Büyükboduk to a quaternionic setting, relaxing the classical \emph{Heegner hypothesis} on the tame conductor of the family. As a byproduct of this construction, we give a proof of one divisibility of the anticyclotomic Iwasawa main conjecture for Hida families. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quaternionic Kolyvagin systems and Iwasawa theory for Hida families Zerman, Francesco Number Theory 11F80, 11R23 We build a modified universal Kolyvagin system for the Galois representation attached to a Hida family of modular forms, starting from the big Heegner point Euler system of Longo--Vigni built in towers of Shimura curves. We generalize the work of Büyükboduk to a quaternionic setting, relaxing the classical \emph{Heegner hypothesis} on the tame conductor of the family. As a byproduct of this construction, we give a proof of one divisibility of the anticyclotomic Iwasawa main conjecture for Hida families. |
| title | Quaternionic Kolyvagin systems and Iwasawa theory for Hida families |
| topic | Number Theory 11F80, 11R23 |
| url | https://arxiv.org/abs/2507.04980 |