Residual supersingular Iwasawa theory and signed Iwasawa invariants

For an odd prime p and a supersingular elliptic curve over a number field, this article introduces a multi-signed residual Selmer group, under certain hypotheses on the base field. This group depends purely on the residual representation at p, yet captures information about the Iwasawa theoretic invariants of the signed p1-Selmer group that arise in supersingular Iwasawa theory. Working in this residual setting provides a natural framework for studying congruences modulo p in Iwasawa theory.