Noncommutative Riemann hypothesis

Tabuada, Gonçalo

doi:10.1090/proc/15874

Noncommutative Riemann hypothesis
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by Gonçalo Tabuada PDF

Proc. Amer. Math. Soc. 150 (2022), 2385-2404 Request permission

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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