On anticyclotomic Euler and Kolyvagin systems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908860733718528 |
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| author | Mastella, Luca Zerman, Francesco |
| author_facet | Mastella, Luca Zerman, Francesco |
| contents | We introduce an axiomatization of the notion of ( $p$-complete) anticyclotomic Euler system for a wide class of Galois representations, including those attached to a cuspidal eigenform and to a Hida family of modular forms. Under a minimal set of assumptions, we show how to build from these data a universal Kolyvagin system for the representation and for its anticyclotomic twist. Eventually, we recover some applications to the structure of Selmer groups and Iwasawa main conjectures and we review a few concrete examples of these abstract notions that can be found in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08710 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On anticyclotomic Euler and Kolyvagin systems Mastella, Luca Zerman, Francesco Number Theory 11F80 (primary), 11R23 (secondary) We introduce an axiomatization of the notion of ( $p$-complete) anticyclotomic Euler system for a wide class of Galois representations, including those attached to a cuspidal eigenform and to a Hida family of modular forms. Under a minimal set of assumptions, we show how to build from these data a universal Kolyvagin system for the representation and for its anticyclotomic twist. Eventually, we recover some applications to the structure of Selmer groups and Iwasawa main conjectures and we review a few concrete examples of these abstract notions that can be found in the literature. |
| title | On anticyclotomic Euler and Kolyvagin systems |
| topic | Number Theory 11F80 (primary), 11R23 (secondary) |
| url | https://arxiv.org/abs/2505.08710 |