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arXiv · 2507.04980

Quaternionic Kolyvagin systems and Iwasawa theory for Hida families

Francesco Zerman
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Abstract

We build a modified universal Kolyvagin system for the Galois representation attached to a Hida family of modular forms, starting from the big Heegner point Euler system of Longo--Vigni built in towers of Shimura curves. We generalize the work of B\"uy\"ukboduk to a quaternionic setting, relaxing the classical \emph{Heegner hypothesis} on the tame conductor of the family. As a byproduct of this construction, we give a proof of one divisibility of the anticyclotomic Iwasawa main conjecture for Hida families.

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Francesco Zerman. 2025-07-07. Quaternionic Kolyvagin systems and Iwasawa theory for Hida families. https://arxiv.org/abs/2507.04980

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