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arXiv · 2505.08710

On anticyclotomic Euler and Kolyvagin systems

Luca Mastella·Francesco Zerman
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Abstract

We introduce an axiomatization of the notion of ( $p$-complete) anticyclotomic Euler system for a wide class of Galois representations, including those attached to a cuspidal eigenform and to a Hida family of modular forms. Under a minimal set of assumptions, we show how to build from these data a universal Kolyvagin system for the representation and for its anticyclotomic twist. Eventually, we recover some applications to the structure of Selmer groups and Iwasawa main conjectures and we review a few concrete examples of these abstract notions that can be found in the literature.

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Luca Mastella, Francesco Zerman. 2026-03-03. On anticyclotomic Euler and Kolyvagin systems. https://doi.org/10.1007/s40316-026-00269-y

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