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.
|Keywords:||Milnor K-theory, Regulator, Abel–Jacobi map, Polylogarithm, Higher Chow group.|
|Full text:||(VoR) Version of Record|
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|Publisher Web site:||http://dx.doi.org/10.1023/B:KTHE.0000006920.60109.e8|
|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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