Classical Motivic Polylogarithm According to Beilinson and Deligne
Classical Motivic Polylogarithm According to Beilinson and Deligne
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根据 Beilinson 和 Deligne 的经典动机多对数
DOI：
10.4171/dm/37-5
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发表时间：
1998
影响因子：
0.9
通讯作者：
J. Wildeshaus
中科院分区：
文献类型：
--
作者：
A. Huber;J. Wildeshaus
本文的主要目的是在射影直线减三点上构造割圆或经典多重对数的动机上同调，并在Deligne或l-adic绝对上同调的调节下，证明其象.通过单位根的特殊化，得到了阿贝尔数ELD的动机上同调和绝对上同调中分圆元的相容性陈述。如[BlK]所示，这种相容性完成了关于黎曼zeta函数特殊值的Tamagawa数猜想的证明。主要的构造和思想包含在Beilinson和Deligne未发表的预印本《动机多对数和Zagier猜想》（[BD 1]）中。我们解决了证明的细节，建立了原始来源中缺失的基础材料：该论文包含一个关于具有系数的绝对霍奇上同调的附录，以及它根据齐藤霍奇模的解释。第二个附录处理K-理论和监管机构的单纯计划。1991年数学科目分类：小学19 F 27;中学11 R 18、11 R 34、11 R 42、14 D 07、14 F 99。
The main purpose of this paper is the construction in motivic cohomology of the cyclotomic, or classical polylogarithm on the projective line minus three points, and the identi cation of its image under the regulator to absolute (Deligne or l-adic) cohomology. By specialization to roots of unity, one obtains a compatibility statement on cyclotomic elements in motivic and absolute cohomology of abelian number elds. As shown in [BlK], this compatibility completes the proof of the Tamagawa number conjecture on special values of the Riemann zeta function. The main constructions and ideas are contained in Beilinson's and Deligne's unpublished preprint \Motivic Polylogarithm and Zagier Conjecture" ([BD1]). We work out the details of the proof, setting up the foundational material which was missing from the original source: the paper contains an appendix on absolute Hodge cohomology with coe cients, and its interpretation in terms of Saito's Hodge modules. The second appendix treats K-theory and regulators for simplicial schemes. 1991 Mathematics Subject Classi cation: Primary 19F27; Secondary 11R18, 11R34, 11R42, 14D07, 14F99.