Zerbes, S;
Loeffler, D;
Skinner, C;
(2019)
Syntomic regulators of Asai–Flach classes.
In:
Proceedings of the Iwasawa 2017.
Mathematical Society of Japan: Tokyo, Japan.
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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.
| Type: | Proceedings paper |
|---|---|
| Title: | Syntomic regulators of Asai–Flach classes |
| Event: | Iwasawa 2017 |
| Location: | Tokyo |
| Dates: | 19 July 2017 - 28 July 2017 |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://www.iwasawa2017.com/ |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10067174 |
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