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dc.contributor.authorTrigo Neri Tabuada, Goncalo Jorge
dc.date.accessioned2018-06-04T19:06:00Z
dc.date.available2018-06-04T19:06:00Z
dc.date.issued2016-09
dc.date.submitted2015-10
dc.identifier.issn2379-1691
dc.identifier.issn2379-1683
dc.identifier.urihttp://hdl.handle.net/1721.1/116068
dc.description.abstractC. Weibel, and Thomason and Trobaugh, proved (under some assumptions) that algebraic K-theory with coefficients is A1-homotopy invariant. We generalize this result from schemes to the broad setting of dg categories. Along the way, we extend the Bass–Quillen fundamental theorem as well as Stienstra’s foundational work on module structures over the big Witt ring to the setting of dg categories. Among other cases, the above A1-homotopy invariance result can now be applied to sheaves of (not necessarily commutative) dg algebras over stacks. As an application, we compute the algebraic K-theory with coefficients of dg cluster categories using solely the kernel and cokernel of the Coxeter matrix. This leads to a complete computation of the algebraic K-theory with coefficients of the du Val singularities parametrized by the simply laced Dynkin diagrams. As a byproduct, we obtain vanishing and divisibility properties of algebraic K-theory (without coefficients). Keywords: A¹-homotopy, algebraic K-theory, Witt vectors, sheaf of dg algebras, dg orbit category, cluster category, du Val singularities, noncommutative algebraic geometryen_US
dc.publisherMathematical Sciences Publishersen_US
dc.relation.isversionofhttp://dx.doi.org/10.2140/AKT.2017.2.1en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleA¹-homotopy invariance of algebraic K-theory with coefficients and du Val singularitiesen_US
dc.typeArticleen_US
dc.identifier.citationTabuada, Gonçalo. “A¹-homotopy invariance of algebraic K-theory with coefficients and du Val singularities.” Annals of K-Theory 2, 1 (January 2017): 1–25 © 2017 Mathematical Sciences Publishersen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorTrigo Neri Tabuada, Goncalo Jorge
dc.relation.journalAnnals of K-Theoryen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2018-05-31T16:02:24Z
dspace.orderedauthorsTabuada, Gonçaloen_US
dspace.embargo.termsNen_US
dc.identifier.orcidhttps://orcid.org/0000-0001-5558-9236
mit.licenseOPEN_ACCESS_POLICYen_US


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