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A regulator formula for Milnor K-groups.

Kerr, M. (2003) 'A regulator formula for Milnor K-groups.', K-Theory., 29 (3). pp. 175-210.


The classical Abel–Jacobi map is used to geometrically motivate the construction of regulator maps from Milnor K-groups K n M (C(X)) to Deligne cohomology. These maps are given in terms of some new, explicit (n – 1)-currents, higher residues of which are defined and related to polylogarithms. We study their behavior in families X s and prove a rigidity result for the regulator image of the Tame kernel, which leads to a vanishing theorem for very general complete intersections.

Item Type:Article
Keywords:Milnor K-theory, Regulator, Abel–Jacobi map, Polylogarithm, Higher Chow group.
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Publisher statement:Reprinted from K-Theory, 29(3), 2003, 175-210 with permission of Kluwer Law International.
Record Created:15 Feb 2008
Last Modified:14 Oct 2016 17:03

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