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

Sohan Ghosh; Jishnu Ray; Takashi Suzuki

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

Number Theory 2025-01-23 v2 Algebraic Geometry

Authors: Sohan Ghosh , Jishnu Ray , Takashi Suzuki

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.

Keywords

iwasawa theory

Cite

@article{arxiv.2407.21431,
  title  = {On $\mu$-invariants and isogenies for abelian varieties over function fields},
  author = {Sohan Ghosh and Jishnu Ray and Takashi Suzuki},
  journal= {arXiv preprint arXiv:2407.21431},
  year   = {2025}
}

Comments

Minor edit. 20 pages

Related papers

View all related →