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