Noncommutative Riemann hypothesis

Goncalo Tabuada

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arXiv · 2105.09935

Noncommutative Riemann hypothesis

Goncalo Tabuada

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Abstract

In this note, making use of noncommutative $l$-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.

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Goncalo Tabuada. 2021-05-20. Noncommutative Riemann hypothesis. https://arxiv.org/abs/2105.09935

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