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On Selmer groups of abelian varieties over ℓ-adic Lie extensions of global function fields

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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 ≠ 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 ∨ has no nontrivial pseudo-null submodule.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze, 53/A, 43124, Parma, Italy

    Andrea Bandini

  2. Dipartimento di Matematica e Informatica, Università della Calabria, Via P. Bucci — Cubo 31B, 87036, Arcavacata di Rende (CS), Italy

    Maria Valentino

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  1. Andrea Bandini
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  2. Maria Valentino
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Correspondence to Andrea Bandini.

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Bandini, A., Valentino, M. On Selmer groups of abelian varieties over ℓ-adic Lie extensions of global function fields. Bull Braz Math Soc, New Series 45, 575–595 (2014). https://doi.org/10.1007/s00574-014-0064-8

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  • DOI: https://doi.org/10.1007/s00574-014-0064-8

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