On $μ$-invariants and isogenies for abelian varieties over function fields
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| Format: | Preprint |
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2024
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| _version_ | 1866929683717685248 |
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| author | Ghosh, Sohan Ray, Jishnu Suzuki, Takashi |
| author_facet | Ghosh, Sohan Ray, Jishnu Suzuki, Takashi |
| contents | We give several formulas for how Iwasawa $μ$-invariants of abelian varieties over unramified $\mathbb{Z}_{p}$-extensions of function fields change under isogeny. These are analogues of Schneider's formula in the number field setting. We also prove that the validity of the Birch--Swinnerton-Dyer conjecture (including the leading coefficient formula) over function fields is invariant under isogeny, without using the result of Kato--Trihan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21431 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $μ$-invariants and isogenies for abelian varieties over function fields Ghosh, Sohan Ray, Jishnu Suzuki, Takashi Number Theory Algebraic Geometry 11R23 (Primary) 11G10, 11R58, 11G40, 14F20 (Secondary) We give several formulas for how Iwasawa $μ$-invariants of abelian varieties over unramified $\mathbb{Z}_{p}$-extensions of function fields change under isogeny. These are analogues of Schneider's formula in the number field setting. We also prove that the validity of the Birch--Swinnerton-Dyer conjecture (including the leading coefficient formula) over function fields is invariant under isogeny, without using the result of Kato--Trihan. |
| title | On $μ$-invariants and isogenies for abelian varieties over function fields |
| topic | Number Theory Algebraic Geometry 11R23 (Primary) 11G10, 11R58, 11G40, 14F20 (Secondary) |
| url | https://arxiv.org/abs/2407.21431 |