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Tabuada, Gonçalo (2022) Noncommutative Riemann hypothesis. Proceedings of the American Mathematical Society, 150 . pp. 2385-2404. doi:10.1090/proc/15874 ISSN 0002-9939.
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Official URL: http://dx.doi.org/10.1090/proc/15874
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.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Riemann hypothesis, Noncommutative differential geometry, Cohomology operations, Geometry, Projective | ||||||
| Journal or Publication Title: | Proceedings of the American Mathematical Society | ||||||
| Publisher: | American Mathematical Society | ||||||
| ISSN: | 0002-9939 | ||||||
| Official Date: | 16 March 2022 | ||||||
| Dates: |
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| Volume: | 150 | ||||||
| Page Range: | pp. 2385-2404 | ||||||
| DOI: | 10.1090/proc/15874 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | First published in Proceedings of the American Mathematical Society in Volume 150, 2022, published by the American Mathematical Society | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Copyright Holders: | © Copyright 2022 American Mathematical Society | ||||||
| Date of first compliant deposit: | 22 March 2022 | ||||||
| Date of first compliant Open Access: | 22 March 2022 | ||||||
| RIOXX Funder/Project Grant: |
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