On the signed Selmer groups of congruent elliptic curves with semistable reduction at all primes above $p$

Abstract

Let $p$ be an odd prime. We attach appropriate signed Selmer groups to an elliptic curve $E$, where $E$ is assumed to have semistable reduction at all primes above $p$. We then compare the Iwasawa $\lambda $-invariants of these signed Selmer groups for tw