A regulator formula for Milnor K-groups

Matt Kerr

doi:10.1023/B:KTHE.0000006920.60109.e8

A regulator formula for Milnor K-groups

Matt Kerr

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	175-210
Number of pages	36
Journal	K-Theory
Volume	29
Issue number	3
DOIs	https://doi.org/10.1023/B:KTHE.0000006920.60109.e8
State	Published - Jul 2003

Keywords

Abel-Jacobi map
Higher Chow group
Milnor K-theory
Polylogarithm
Regulator

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10.1023/B:KTHE.0000006920.60109.e8

Cite this

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AB - The classical Abel-Jacobi map is used to geometrically motivate the construction of regulator maps from Milnor K-groups Kn 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.

KW - Abel-Jacobi map

KW - Higher Chow group

KW - Milnor K-theory

KW - Polylogarithm

KW - Regulator

UR - https://www.scopus.com/pages/publications/3543014408

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JO - K-Theory

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A regulator formula for Milnor K-groups

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Keywords

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