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Title: | Additive invariants of orbifolds | Authors: | Tabuada, Goncalo VAN DEN BERGH, Michel |
Issue Date: | 2018 | Publisher: | GEOMETRY & TOPOLOGY PUBLICATIONS | Source: | GEOMETRY & TOPOLOGY, 22(5), p. 3003-3048 | 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second author and Polishchuk concerning Hochschild homology, and of Baranovsky and Petrov, and Caldararu and Arinkin (unpublished), concerning twisted Hochschild homology; in the case of topological Hochschild homology and periodic topological cyclic homology, the aforementioned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. | Notes: | [Tabuada, Goncalo] MIT, Dept Math, Cambridge, MA 02139 USA. [Tabuada, Goncalo] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, Lisbon, Portugal. [Tabuada, Goncalo] Univ Nova Lisboa, Fac Ciencias & Tecnol, Ctr Matemat & Aplicacoes, Lisbon, Portugal. [Van den Bergh, Michel] Univ Hasselt, Dept Math, Diepenbeek, Belgium. | Keywords: | orbifold; algebraic K–theory; cyclic homology; topological Hochschild homology; Azumaya algebra; standard conjectures; noncommutative algebraic geometry | Document URI: | http://hdl.handle.net/1942/28511 | ISSN: | 1465-3060 | e-ISSN: | 1364-0380 | DOI: | 10.2140/gt.2018.22.3003 | ISI #: | 000434786500012 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2019 |
Appears in Collections: | Research publications |
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