Asai-Flach类的联组调节子
Syntomic regulators of Asai--Flach classes
摘要：
本文导出了Asai-Flach类的p-adic同分调节子的一个公式。这些是上同调类形成一个欧拉系统相关的希尔伯特模形式在二次域，介绍了在较早的文件（arXiv：1607.07813）安东尼奥雷和第一和第三作者。我们在这里开发的公式表示的微分算子作用于过收敛的希尔伯特模形式，它是类似于现有的公式的监管机构的贝林森-Flach类，但一个新的功能是外观的一个投影算子相关联的临界斜率爱森斯坦系列。最后，我们得出结论的文件与数值计算给出了强有力的证据，这些监管机构的非零的一个明确的例子。
英文摘要：
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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