The Asai--Flach Euler system in $p$-adic families
Number Theory
2025-06-25 v1
Abstract
We show that the Euler system for the Asai representation corresponding to a Hilbert modular eigenform over a real quadratic field, constructed by Lei, Loeffler and Zerbes (2018), can be interpolated -adically as the Hilbert modular form varies in a Hida family. This work is used as an important input in recent work of Grossi, Loeffler and Zerbes (2025) on the proof of the Bloch--Kato conjecture in analytic rank zero for the Asai representation.
Cite
@article{arxiv.2506.19673,
title = {The Asai--Flach Euler system in $p$-adic families},
author = {David Loeffler and Arshay Sheth},
journal= {arXiv preprint arXiv:2506.19673},
year = {2025}
}
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