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 p^\infty -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.