论文标题
聚类和shintani生成类的杂物实现完全真实的领域
The Hodge Realization of the Polylogarithm and the Shintani Generating Class for Totally Real Fields
论文作者
论文摘要
在本文中，我们构建了与完全真实领域相关的某些代数圆环的杂物类别的杂物级别的实现。然后，我们证明了该聚集体的DE RHAM实现给出了Shintani生成类，这是一种共同体类别，生成了非阳性整数上完全真实领域的LERCH ZETA函数的值。受此结果的启发，我们提出了一个关于在扭转点的专业化类别的专业化的猜想，并讨论了其与贝林森猜想的关系的关系。
In this article, we construct the Hodge realization of the polylogarithm class in the equivariant Deligne-Beilinson cohomology of a certain algebraic torus associated to a totally real field. We then prove that the de Rham realization of this polylogarithm gives the Shintani generating class, a cohomology class generating the values of the Lerch zeta functions of the totally real field at nonpositive integers. Inspired by this result, we give a conjecture concerning the specialization of this polylogarithm class at torsion points, and discuss its relation to the Beilinson conjecture for Hecke characters of totally real fields.
