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

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.

Accepted for publication in Mathematische Annalen. 26 pages