Regulator Maps for Higher Chow Groups via Current Transforms

Pedro F. dos Santos; Robert M. Hardt; Paulo Lima-Filho

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arXiv · 1903.11541

Regulator Maps for Higher Chow Groups via Current Transforms

Pedro F. dos Santos·Robert M. Hardt·Paulo Lima-Filho

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Abstract

We show how to use equidimensional algebraic correspondences between complex algebraic varieties to construct pull-backs and transforms of certain classes of geometric currents. Using this construction we produce explicit formulas at the level of complexes for a regulator map from the Higher Chow groups of smooth complex quasi-projective algebraic varieties to Deligne-Beilinson cohomology with integral coefficients. A distinct aspect of our approach is the use of Suslin's complex of equidimensional cycles over $ \Delta^n $ to compute Bloch's higher Chow groups. We calculate explicit examples involving the M\"{a}hler measure of Laurent polynomials.

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Pedro F. dos Santos, Robert M. Hardt, Paulo Lima-Filho. 2019-03-27. Regulator Maps for Higher Chow Groups via Current Transforms. https://arxiv.org/abs/1903.11541

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