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A regulator formula for Milnor K-groups

Kerr, M.

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Authors

M. Kerr



Abstract

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.

Citation

Kerr, M. (2003). A regulator formula for Milnor K-groups. K-Theory, 29(3), 175-210. https://doi.org/10.1023/b%3Akthe.0000006920.60109.e8

Journal Article Type Article
Publication Date Jul 1, 2003
Deposit Date Feb 15, 2008
Publicly Available Date Oct 14, 2016
Journal K-Theory
Print ISSN 0920-3036
Electronic ISSN 1573-0514
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 29
Issue 3
Pages 175-210
DOI https://doi.org/10.1023/b%3Akthe.0000006920.60109.e8
Keywords Milnor K-theory, Regulator, Abel–Jacobi map, Polylogarithm, Higher Chow group.

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Copyright Statement
Reprinted from K-Theory, 29(3), 2003, 175-210 with permission of Kluwer Law International.




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