MIT 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.

A¹-homotopy invariants of dg orbit categories

Author(s)
Trigo Neri Tabuada, Goncalo Jorge
Thumbnail
DownloadTabuada_A1-homotopy.pdf (265.2Kb)
PUBLISHER_CC

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 A be a dg category, F : A →A be a dg functor inducing an equivalence of categories in degree-zero cohomology, and A /F be the associated dg orbit category. For every A¹-homotopy invariant E ( e.g. homotopy K -theory, K -theory with coefficients, étale K-theory, and periodic cyclic homology), we construct a distinguished triangle expressing E ( A /F )as the cone of the endomorphism E ( F ) − Id of E ( A ). In the particular case where F is the identity dg functor, this triangle splits and gives rise to the fundamental theorem. As a first application, we compute the A¹-homotopy invariants of cluster (dg) categories, and consequently of Kleinian singularities, using solely the Coxeter matrix. As a second application, we compute the A¹-homotopy invariants of the dg orbit categories associated with Fourier–Mukai autoequivalences.
Date issued
2015-04
URI
http://hdl.handle.net/1721.1/116259
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Journal of Algebra
Publisher
Elsevier
Citation
Tabuada, Gonçalo. “A¹-homotopy invariants of dg orbit categories.” Journal of Algebra 434 (July 2015): 169–192.
Version: Original manuscript
ISSN
00218693

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
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.