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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2005.02520 |
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| _version_ | 1866913235290030080 |
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| author | Fornea, Michele Jin, Zhaorong |
| author_facet | Fornea, Michele Jin, Zhaorong |
| contents | Conditionally on a conjecture on the étale cohomology of Hilbert modular surfaces and some minor technical assumptions, we establish new instances of the equivariant BSD-conjecture in rank $0$ with applications to the arithmetic of rational elliptic curves over quintic fields. The key ingredients are a refinement of twisted triple product $p$-adic $L$-functions, the construction of a compatible collection of Hirzebruch-Zagier cycles and an explicit reciprocity law relating the two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_02520 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Hirzebruch-Zagier classes and rational elliptic curves over quintic fields Fornea, Michele Jin, Zhaorong Number Theory Conditionally on a conjecture on the étale cohomology of Hilbert modular surfaces and some minor technical assumptions, we establish new instances of the equivariant BSD-conjecture in rank $0$ with applications to the arithmetic of rational elliptic curves over quintic fields. The key ingredients are a refinement of twisted triple product $p$-adic $L$-functions, the construction of a compatible collection of Hirzebruch-Zagier cycles and an explicit reciprocity law relating the two. |
| title | Hirzebruch-Zagier classes and rational elliptic curves over quintic fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2005.02520 |