English

The Riemann-Roch Theorem on higher dimensional complex noncommutative tori

Operator Algebras 2023-05-19 v1 Algebraic Geometry K-Theory and Homology

Abstract

We prove analogues of the Riemann-Roch Theorem and the Hodge Theorem for noncommutative tori (of any dimension) equipped with complex structures, and discuss implications for the question of how to distinguish "noncommutative abelian varieties" from "non-algebraic" noncommutative complex tori.

Keywords

Cite

@article{arxiv.1907.10200,
  title  = {The Riemann-Roch Theorem on higher dimensional complex noncommutative tori},
  author = {Varghese Mathai and Jonathan Rosenberg},
  journal= {arXiv preprint arXiv:1907.10200},
  year   = {2023}
}

Comments

15 pages

R2 v1 2026-06-23T10:28:57.115Z