English

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

R2 v1 2026-06-22T10:53:02.373Z