论文标题
Shimura品种的回火电流和Deligne共同体，并应用于$ \ mathrm {gsp} _6 $
Tempered currents and Deligne cohomology of Shimura varieties, with an application to $\mathrm{GSp}_6$
论文作者
论文摘要
我们为任何Shimura品种在钢流方面提供了对Deligne-Beilinson的新描述。这对于计算动机阶层的调节因子以及贝林森猜想的研究特别有用。作为应用程序，我们在中间程度上构建类，以及Siegel六倍的一种动机共同体，并根据Rankin-Selberg型自动形态积分来计算Beilinson较高调节剂的形象。使用Pollack和Shah的结果，我们将积分与Beilinson猜想所预测的那样，将积分与$ 8 $ spin $ l $ functions的非关键特殊值联系起来。
We provide a new description of Deligne-Beilinson cohomology for any Shimura variety in terms of tempered currents. This is particularly useful for computations of regulators of motivic classes and hence to the study of Beilinson conjectures. As an application, we construct classes in the middle degree plus one motivic cohomology of Siegel sixfolds and we compute their image by Beilinson higher regulator in terms of Rankin-Selberg type automorphic integrals. Using results of Pollack and Shah, we relate the integrals to noncritical special values of the degree $8$ Spin $L$-functions, as predicted by Beilinson conjectures.
