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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.19673 |
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| _version_ | 1866916809859399680 |
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| author | Loeffler, David Sheth, Arshay |
| author_facet | Loeffler, David Sheth, Arshay |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19673 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Asai--Flach Euler system in $p$-adic families Loeffler, David Sheth, Arshay Number Theory 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. |
| title | The Asai--Flach Euler system in $p$-adic families |
| topic | Number Theory |
| url | https://arxiv.org/abs/2506.19673 |