M. Kerr
A regulator formula for Milnor K-groups
Kerr, M.
Authors
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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