Functional equations for supersingular abelian varieties over Z_p²-extensions

2022/08/02 by Dion, Cédric
#11R23 (Primary) 11F80 #14K05 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2208.01474

Abstract

Let K be an imaginary quadratic field and K_∞ be the Z_p²-extension of K. Answering a question of Ahmed and Lim, we show that the Pontryagin dual of the Selmer group associated to a supersingular polarized abelian variety admits an algebraic functional equation. The proof uses the theory of Γ-system developed by Lai, Longhi, Tan and Trihan. We also show the algebraic functional equation holds for Sprung's chromatic Selmer groups of supersingular elliptic curves along K_∞.

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