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arXiv · 2506.19673

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

David Loeffler·Arshay Sheth
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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 $p$-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.

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David Loeffler, Arshay Sheth. 2025-06-24. The Asai--Flach Euler system in $p$-adic families. https://arxiv.org/abs/2506.19673

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