Regulators and cycle maps in higher-dimensional differential algebraic K-theory
Number Theory
2015-09-28 v5 Algebraic Geometry
K-Theory and Homology
Abstract
We develop differential algebraic K-theory of regular arithmetic schemes. Our approach is based on a new construction of a functorial, spectrum level Beilinson regulator using differential forms. We construct a cycle map which represents differential algebraic K-theory classes by geometric vector bundles. As an application we derive Lott's relation between short exact sequences of geometric bundles with a higher analytic torsion form.
Cite
@article{arxiv.1209.6451,
title = {Regulators and cycle maps in higher-dimensional differential algebraic K-theory},
author = {Ulrich Bunke and Georg Tamme},
journal= {arXiv preprint arXiv:1209.6451},
year = {2015}
}
Comments
106 pages (corrects a mistake in the sheaf condition), published version