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Syntomic regulators of Asai–Flach classes
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Loeffler, David, Skinner, Christopher and Zerbes, Sarah Livia (2021) Syntomic regulators of Asai–Flach classes. In: Iwasawa 2017: Development of Iwasawa Theory — the Centennial of K. Iwasawa's Birth, Tokyo, Japan, 19-28 Jul 2017. Published in: Advanced Studies in Pure Mathematics, 86 pp. 595-638. doi:10.2969/aspm/08610595 ISSN 0920-1971.
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WRAP-syntomic-regulators-Asai–Flach-classes-Loeffler-2018.pdf - Accepted Version - Requires a PDF viewer. Download (742Kb) | Preview |
Official URL: http://dx.doi.org/10.2969/aspm/08610595
Abstract
In this paper, we derive a formula for the p-adic syntomic regulators of Asai–Flach classes. These are cohomology classes forming an Euler system associated to a Hilbert modular form over a quadratic field, introduced in an earlier paper [LLZ16] by Antonio Lei and the first and third authors. The formula we develop here is expressed in terms of differential operators acting on overconvergent Hilbert modular forms; it is analogous to existing formulae for the regulators of Beilinson–Flach classes, but a novel feature is the appearance of a projection operator associated to a critical-slope Eisenstein series. We conclude the paper with numerical calculations giving strong evidence for the non-vanishing of these regulators in an explicit example.
| Item Type: | Conference Item (Paper) | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Hilbert modular surfaces, Forms, Modular, L-functions, P-adic numbers, Algebraic number theory | |||||||||
| Journal or Publication Title: | Advanced Studies in Pure Mathematics | |||||||||
| Publisher: | Mathematical Society of Japan | |||||||||
| ISSN: | 0920-1971 | |||||||||
| Editor: | Kurihara, M. and Bannai, K. and Ochiai, T. and Tsuji, T. | |||||||||
| Official Date: | 12 January 2021 | |||||||||
| Dates: |
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| Volume: | 86 | |||||||||
| Page Range: | pp. 595-638 | |||||||||
| DOI: | 10.2969/aspm/08610595 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | Papers which appeared in ASPM vol. 86 | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 16 January 2019 | |||||||||
| Date of first compliant Open Access: | 25 January 2021 | |||||||||
| RIOXX Funder/Project Grant: |
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| Conference Paper Type: | Paper | |||||||||
| Title of Event: | Iwasawa 2017: Development of Iwasawa Theory — the Centennial of K. Iwasawa's Birth | |||||||||
| Type of Event: | Conference | |||||||||
| Location of Event: | Tokyo, Japan | |||||||||
| Date(s) of Event: | 19-28 Jul 2017 | |||||||||
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