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

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.

arXiv comment34 pages. This replaces the two previously separate documents, "On the Bloch-Kato conjecture and Iwasawa main conje cture for GO(4)" (version 1 of this Arxiv preprint) and "Asai-Flach classes and p-adic L-functions" (2309.07536), which are now merged together. arXiv admin note: substantial text overlap with arXiv:2309.07536