Residual supersingular Iwasawa theory and signed Iwasawa invariants

Filippo A. E. Nuccio; Ramdorai Sujatha

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arXiv · 1911.10649

Residual supersingular Iwasawa theory and signed Iwasawa invariants

Filippo A. E. Nuccio·Ramdorai Sujatha

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Abstract

For an odd prime $p$ and a supersingular elliptic curve over a number field, this article introduces a fine 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.

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Filippo A. E. Nuccio, Ramdorai Sujatha. 2019-11-25. Residual supersingular Iwasawa theory and signed Iwasawa invariants. https://arxiv.org/abs/1911.10649

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