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arXiv · 2407.21431

On $\mu$-invariants and isogenies for abelian varieties over function fields

Sohan Ghosh·Jishnu Ray·Takashi Suzuki
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Abstract

We give several formulas for how Iwasawa $\mu$-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.

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Sohan Ghosh, Jishnu Ray, Takashi Suzuki. 2024-07-31. On $\mu$-invariants and isogenies for abelian varieties over function fields. https://doi.org/10.1007/s00208-026-03535-0

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