Multiplicative properties of the current transform regulator

Author:

Paulo Lima-Filho

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), K-Theory and Homology (math.KT)

journal:

date:

2023-07-07 16:00:00

Abstract

This paper utilizes the properties of transforms of currents under equidimensional cycles, as introduced in \cite{MR4498559}, to establish the multiplicative nature of the resulting regulator map, in the derived category. The construction relies on a synthetic presentation of the fundamental triples of currents from \cite{MR4498559}, which exhibits group-like behavior under an extended Eilenberg-Zilber morphism. A key component of the analysis is a character of the permutation Hopf algebra that takes values in the function field of an infinite-dimensional affine space.

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