On the algebraic functional equation for the mixed signed Selmer group over multiple ${\mathbb{Z}}_p$-extensions

Abstract

Let $E$ be an elliptic curve defined over a number field with good reduction at all primes above a fixed odd prime $p$, where at least one of which is a supersingular prime of $E$. In this paper, we will establish the algebraic functional equation for the mixed signed Selmer groups of an elliptic curve with good reduction at every prime above $p$ over a multiple ${\mathbb{Z}}_p$-extension.

References in corpus (2)

• Akashi series and Euler characteristics of signed Selmer groups of elliptic curves with semistable reduction at primes above p
• On the algebraic functional equation of the eigenspaces of mixed signed Selmer groups of elliptic curves with good reduction at primes above $p$