Fredholm modules and the Beilinson-Bloch regulator
Operator Algebras
2015-09-24 v2 Algebraic Geometry
Abstract
We prove an operator-theoretic reconstruction of the Beilinson-Bloch regulator for compact Riemann surfaces, using loop operators and the Connes-Karoubi character for Fredholm modules. The proof includes a new computation of the Connes-Karoubi character for Steinberg symbols of the circle, which relies on the Helton-Howe determinant theory, but not on the Carey-Pincus theory of joint torsion.
Cite
@article{arxiv.1509.02864,
title = {Fredholm modules and the Beilinson-Bloch regulator},
author = {Eugene Ha and Victor Kasatkin},
journal= {arXiv preprint arXiv:1509.02864},
year = {2015}
}
Comments
21 pages. V2: Proof of Prop. 1 simplified, minor improvements to exposition