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An Euler system for the adjoint of a modular form

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arxiv 2312.04665 v2 pith:BCOQFGVA submitted 2023-12-07 math.NT

David Loeffler , Sarah Livia Zerbes This is my paper · ORCID
classification math.NT
keywords adjointeulermodularsystemformrepresentationagreesarising
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We construct an Euler system for the adjoint Galois representation of a modular form, using motivic cohomology classes arising from Hilbert modular surfaces. We use this Euler system to give an upper bound for the Selmer group of the adjoint representation over the cyclotomic Zp-extension, which agrees with the predictions of the Iwasawa main conjecture up to powers of p.

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  1. An anticyclotomic Euler system of Hirzebruch--Zagier cycles I: Norm relations and $p$-adic interpolation

    math.NT 2025-01 conditional novelty 7.0 of 10

    Constructs a new anticyclotomic Euler system for Asai Galois representations attached to p-ordinary Hilbert modular forms, with norm relations and p-adic interpolation.

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