English

Noncommutative Riemann hypothesis

Algebraic Geometry 2021-05-21 v1 Algebraic Topology K-Theory and Homology Representation Theory

Abstract

In this note, making use of noncommutative ll-adic cohomology, we extend the generalized Riemann hypothesis from the realm of algebraic geometry to the broad setting of geometric noncommutative schemes in the sense of Orlov. As a first application, we prove that the generalized Riemann hypothesis is invariant under derived equivalences and homological projective duality. As a second application, we prove the noncommutative generalized Riemann hypothesis in some new cases.

Keywords

Cite

@article{arxiv.2105.09935,
  title  = {Noncommutative Riemann hypothesis},
  author = {Goncalo Tabuada},
  journal= {arXiv preprint arXiv:2105.09935},
  year   = {2021}
}

Comments

13 pages

R2 v1 2026-06-24T02:18:55.467Z