Syntomic regulators of Asai--Flach classes
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 (arXiv:1607.07813) 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.
Keywords
Cite
@article{arxiv.1608.06112,
title = {Syntomic regulators of Asai--Flach classes},
author = {David Loeffler and Christopher Skinner and Sarah Livia Zerbes},
journal= {arXiv preprint arXiv:1608.06112},
year = {2021}
}
Comments
Revised version: strengthened main theorem to avoid unnecessary assumptions, and added a formula for normalisation of Eisenstein functional