Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 118, 12 pages      arXiv:1805.04646      https://doi.org/10.3842/SIGMA.2018.118
Contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko Yui

Integral Regulators for Higher Chow Complexes

Muxi Li
University of Science and Technology, Hefei, Anhui, P.R. China

Received May 12, 2018, in final form October 31, 2018; Published online November 03, 2018

Abstract
Building on Kerr, Lewis and Müller-Stach's work on the rational regulator, we prove the existence of an integral regulator on higher Chow complexes and give an explicit expression. This puts firm ground under some earlier results and speculations on the torsion in higher cycle groups by Kerr-Lewis-Müller-Stach, Petras, and Kerr-Yang.

Key words: integral regulator; higher Chow groups; algebraic cycles; Abel-Jacobi map.

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References

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