MIT Libraries homeMIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Noncommutative motives in positive characteristic and their applications

Author(s)
Tabuada, Gonçalo
Thumbnail
DownloadSubmitted version (Embargoed until: 2021-06-20, 419.2Kb)
Publisher with Creative Commons License

Publisher with Creative Commons License

Creative Commons Attribution

Terms of use
Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/
Metadata
Show full item record
Abstract
Let k be a base field of positive characteristic. Making use of topological periodic cyclic homology, we start by proving that the category of noncommutative numerical motives overkis abelian semi-simple, as conjecturedby Kontsevich. Then, we establish a far-reaching noncommutative generaliza-tion of the Weil conjectures, originally proved by Dwork andGrothendieck. Inthe same vein, we establish a far-reaching noncommutative generalization of the cohomological interpretations of the Hasse-Weil zeta function, originallyproven by Hesselholt. As a third main result, we prove that the numericalGrothendieck group of every smooth proper dg category is a finitely generatedfree abelian group, as claimed (without proof) by Kuznetsov. Then, we introduce the noncommutative motivic Galois (super-)groupsand, following aninsight of Kontsevich, relate them to their classical commutative counterparts.Finally, we explain how the motivic measure induced by Berthelot’s rigid cohomology can be recovered from the theory of noncommutativemotives.
Date issued
2019-06
URI
https://hdl.handle.net/1721.1/126181
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Advances in mathematics
Publisher
Elsevier BV
Citation
Tabuada, Gonçalo. “Noncommutative motives in positive characteristic and their applications.” Advances in mathematics, vol. 349, 2019, pp. 648-681 © 2019 The Author
Version: Original manuscript
ISSN
0001-8708

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries homeMIT Libraries logo

Find us on

Twitter Facebook Instagram YouTube RSS

MIT Libraries navigation

SearchHours & locationsBorrow & requestResearch supportAbout us
PrivacyPermissionsAccessibility
MIT
Massachusetts Institute of Technology
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.