Multiplicative properties of the current transform regulator
Algebraic Geometry
2023-07-11 v1 K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.2307.03991,
title = {Multiplicative properties of the current transform regulator},
author = {Paulo Lima-Filho},
journal= {arXiv preprint arXiv:2307.03991},
year = {2023}
}