English

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 pp-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.

Keywords

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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R2 v1 2026-07-01T03:31:43.693Z