On Selmer groups of abelian varieties over $\ell$-adic Lie extensions of global function fields

Abstract

Let $F$ be a global function field of characteristic $p>0$ and $A/F$ an abelian variety. Let $K/F$ be an $ł$-adic Lie extension ($ł\ne p$) unramified outside a finite set of primes $S$ and such that $\Gal(K/F)$ has no elements of order $ł$. We shall prove that, under certain conditions, $Se{l}_A(K{)}_{ł}^{\vee }$ has no nontrivial pseudo-null submodule.

arXiv comment14 pages

References in corpus (1)

• Control Theorems for l-adic Lie extensions of global function fields