Growth of Selmer Groups over function fields

Abstract

We study the rank of the $p$-Selmer group $Se{l}_p(A/k)$ of an abelian variety $A/k$, where $k$ is a function field. If $K/k$ is a quadratic extension and $F/k$ is a dihedral extension and the ${\mathbb{Z}}_p$-corank of $Se{l}_p(A/K)$ is odd, we show that the ${\mathbb{Z}}_p$-corank of $Se{l}_p(A/F)\ge [F:K]$. The result uses the theory of local constants developed by Mazur-Rubin for elliptic curves over number fields.

This paper has been withdrawn by the author due to a mistaken assumption about local Tate duality

References in corpus (1)

• Regulator constants and the parity conjecture