Akashi series and Euler characteristics of signed Selmer groups of elliptic curves with semistable reduction at primes above p

Abstract

Let $p$ be an odd prime number, and let $E$ be an elliptic curve defined over a number field $F^{\prime }$ such that $E$ has semistable reduction at every prime of $F^{\prime }$ above $p$ and is supersingular at at least one prime above $p$. Under appropriate hypotheses, we compute the Akashi series of the signed Selmer groups of $E$ over a ${\mathbb{Z}}_p^d$-extension over a finite extension $F$ of $F^{\prime }$. As a by-product, we also compute the Euler characteristics of these Selmer groups.

Some minor corrections and revisions; 19 pages

References in corpus (5)

• On the growth of Mordell-Weil ranks in $p$-adic Lie extensions
• On the Euler characteristics of signed Selmer groups
• Mordell-Weil ranks and Tate-Shafarevich groups of elliptic curves with mixed-reduction type over cyclotomic extensions
• On Selmer groups in the supersingular reduction case
• On the plus and the minus Selmer groups for elliptic curves at supersingular primes

Cited by in corpus (1)

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