Additive invariants of orbifolds
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gt-v22-n5-p12-s.pdf
Description
Published version
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668.59 KB
Format
Adobe PDF
Checksum (MD5)
413424c282174ba6d2255b41d2171cf4
Author(s)
Tabuada, Gonçalo
Van den Bergh, Michel
Date Issued
June 2018
Journal
Geometry & Topology
Publisher
Mathematical Sciences Publishers
Citation
Tabuada, Gonçalo and Van den Bergh, Michel. "Additive invariants of orbifolds." Geometry & Topology 22, 5 (2018): 3003–3048 © 2018 Mathematical Science Publishers
Version
Final published version
Abstract
Using the recent theory of noncommutative motives, we compute the additive invariants of orbifolds (equipped with a sheaf of Azumaya algebras) using solely “fixed-point data”. As a consequence, we recover, in a unified and conceptual way, the original results of Vistoli concerning algebraic K–theory, of Baranovsky concerning cyclic homology, of the second author and Polishchuk concerning Hochschild homology, and of Baranovsky and Petrov, and Cǎldǎraru and Arinkin (unpublished), concerning twisted Hochschild homology; in the case of topological Hochschild homology and periodic topological cyclic homology, the aforementioned computation is new in the literature. As an application, we verify Grothendieck’s standard conjectures of type C+ and D, as well as Voevodsky’s smash-nilpotence conjecture, in the case of “low-dimensional” orbifolds. Finally, we establish a result of independent interest concerning nilpotency in the Grothendieck ring of an orbifold. Keywords: orbifold; algebraic K–theory; cyclic homology; topological Hochschild homology; Azumaya algebra; standard conjectures; noncommutative algebraic geometry
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.2140/GT.2018.22.3003
