On Euler characteristics of Selmer groups for abelian varieties over global function fields

Abstract

Let $F$ be a global function field of characteristic $p>0$, $K/F$ an $\ell$-adic Lie extension ($\ell \ne p$) and $A/F$ an abelian variety. We provide Euler characteristic formulas for the $Gal(K/F)$-module $Se{l}_A(K{)}_{\ell }$.

arXiv commentTo appear in Arch. Math. (Basel)