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arXiv · 1608.06112

Syntomic regulators of Asai--Flach classes

David Loeffler·Christopher Skinner·Sarah Livia Zerbes
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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 (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.

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David Loeffler, Christopher Skinner, Sarah Livia Zerbes. 2016-08-22. Syntomic regulators of Asai--Flach classes. https://doi.org/10.2969/aspm%2F08610595

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