A commutative regulator map into Deligne–Beilinson cohomology

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• 作者：Thomas Weißschuh
• 关键词：Mathematics Subject Classification14C25 ; 32C30
• 刊名：manuscripta mathematica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：152
• 期：3-4
• 页码：281-315
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1785
• 卷排序：152

文摘

Bloch (The Lefschetz centennial conference, part I (Mexico City, 1984), volume 58 of contemporary mathematics. American Mathematical Society, Providence, pp 65–79, 1986) gave an abstract definition of a map (regulator) from higher Chow groups to Deligne–Beilinson cohomology. This map can be defined on the underlying complexes, and Kerr et al. (Compos Math 142:374–396, 2006) gave an explicit description of this map in terms of currents. Using a multiplicative version of the Deligne complex, we give a commutative version of the above map.