For an odd prime 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 , yet captures information about the Iwasawa theoretic invariants of the signed -Selmer group that arise in supersingular Iwasawa theory. Working in this residual setting provides a natural framework for studying congruences modulo in Iwasawa theory.
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Filippo A. E. Nuccio Mortarino Majno di Capriglio, Sujatha Ramdorai, Residual supersingular Iwasawa theory and signed Iwasawa invariants. Rend. Sem. Mat. Univ. Padova 149 (2023), pp. 83–129DOI 10.4171/RSMUP/111