On the cohomology of plus/minus Selmer groups of supersingular elliptic curves in weakly ramified base fields

TL;DR

This paper extends the understanding of signed Selmer groups of supersingular elliptic curves over weakly ramified fields, proving Kida's formula and integrality of characteristic elements in this context.

Contribution

It generalizes previous results to weakly ramified base fields, providing new proofs of Kida's formula and integrality for signed Selmer groups.

Findings

Proves Kida's formula for signed Selmer groups in weakly ramified extensions.

Establishes integrality of characteristic elements for these Selmer groups.

Extends known results from unramified to weakly ramified settings.

Abstract

Let $E/\mathbb{Q}$ be an elliptic curve and let $p\ge 5$ be a prime of good supersingular reduction. We generalize results due to Meng Fai Lim proving Kida's formula and integrality results for characteristic elements of signed Selmer groups along the cyclotomic $\mathbb{Z}_p$-extension of weakly ramified base fields $K/\mathbb{Q}_p$.