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Stark-Heegner cycles attached to Bianchi modular forms
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Venkat, Guhan and Williams, Christopher David (2021) Stark-Heegner cycles attached to Bianchi modular forms. Journal of the London Mathematical Society, 104 (1). pp. 394-422. doi:10.1112/jlms.12438 ISSN 0024-6107.
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WRAP-Stark-Heegner-cycles-attached-Bianchi-modular-2021.pdf - Accepted Version - Requires a PDF viewer. Download (1096Kb) | Preview |
Official URL: https://doi.org/10.1112/jlms.12438
Abstract
Let f be a Bianchi modular form, that is, an automorphic form for GL(2) over an imaginary quadratic field F, and let P be a prime of F at which f is new. Let K be a quadratic extension of F, and L(f/K,s) the L-function of the base-change of f to K. Under certain hypotheses on f and K, the functional equation of L(f/K,s) ensures that it vanishes at the central point. The Bloch--Kato conjecture predicts that this should force the existence of non-trivial classes in an appropriate global Selmer group attached to f and K. In this paper, we use the theory of double integrals developed by Barrera Salazar and the second author to construct certain P-adic Abel--Jacobi maps, which we use to propose a construction of such classes via "Stark--Heegner cycles". This builds on ideas of Darmon and in particular generalises an approach of Rotger and Seveso in the setting of classical modular forms.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Bianchi groups, Forms, Modular, p-adic numbers , Multiple integrals | |||||||||
| Journal or Publication Title: | Journal of the London Mathematical Society | |||||||||
| Publisher: | Wiley Publishing Ltd. | |||||||||
| ISSN: | 0024-6107 | |||||||||
| Official Date: | July 2021 | |||||||||
| Dates: |
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| Volume: | 104 | |||||||||
| Number: | 1 | |||||||||
| Page Range: | pp. 394-422 | |||||||||
| DOI: | 10.1112/jlms.12438 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | This is the accepted version of the following article: Venkat, G. and Williams, C. (2021), Stark–Heegner cycles attached to Bianchi modular forms. J. London Math. Soc.. https://doi.org/10.1112/jlms.12438, which has been published in final form at https://doi.org/10.1112/jlms.12438 | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 13 January 2021 | |||||||||
| Date of first compliant Open Access: | 22 January 2021 | |||||||||
| RIOXX Funder/Project Grant: |
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