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Asai-Flach classes, p-adic L-functions and the Bloch-Kato conjecture for GO(4)

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arxiv 2407.17055 v2 pith:6XMCLBTL submitted 2024-07-24 math.NT

Giada Grossi , David Loeffler , Sarah Livia Zerbes This is my paper · ORCID
classification math.NT
keywords conjecturel-functionsbloch-katoformshilbertmodularp-adicprove
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We prove the Bloch-Kato conjecture for critical values of Asai L-functions of p-ordinary Hilbert modular forms over quadratic fields (with p split); and one inclusion in the Iwasawa main conjecture for these L-functions (up to a power of p). Along the way, we also prove a version of the p-adic Eichler-Shimura comparison isomorphism for Hida families of Hilbert modular forms.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. New perspectives on $p$-adic regulator formulae

    math.NT 2026-01 conditional novelty 6.0 of 10

    A finite-slope p-adic regulator formula for Asai–Flach classes is proved without finite-polynomial cohomology, and diagonal classes are reconstructed as pullback extension classes.

  2. The Asai--Flach Euler system in $p$-adic families

    math.NT 2025-06 conditional novelty 6.0 of 10

    The Asai-Flach Euler system of Lei-Loeffler-Zerbes is interpolated p-adically over Hida families of Hilbert modular forms over real quadratic fields.

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