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

· 2024 · math.NT · arXiv 2407.17055

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abstract

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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math.NT 1

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2025 1

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

math.NT · 2025-06-24 · conditional · novelty 6.0

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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  • The Asai--Flach Euler system in $p$-adic families math.NT · 2025-06-24 · conditional · none · ref 8 · internal anchor

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