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

Andrea Bandini; Maria Valentino

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

Number Theory 2013-07-10 v1

Authors: Andrea Bandini , Maria Valentino

Abstract

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

Keywords

Selmer groups abelian varieties global function fields l-adic Lie extensions pseudo-null submodule Galois groups arithmetic geometry

Cite

@article{arxiv.1307.2441,
  title  = {On Selmer groups of abelian varieties over $\ell$-adic Lie extensions of global function fields},
  author = {Andrea Bandini and Maria Valentino},
  journal= {arXiv preprint arXiv:1307.2441},
  year   = {2013}
}

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14 pages

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

Abstract

Keywords

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