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.

The Gysin triangle via localization and A[superscript 1]-homotopy invariance

Author(s)
Van den Bergh, Michel; Trigo Neri Tabuada, Goncalo Jorge
Thumbnail
DownloadS0002-9947-2017-06956-7.pdf (428.0Kb)
PUBLISHER_POLICY

Publisher Policy

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.

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.
Metadata
Show full item record
Abstract
Let X be a smooth scheme, Z a smooth closed subscheme, and U the open complement. Given any localizing and A[superscript 1]-homotopy invariant of dg categories E, we construct an associated Gysin triangle relating the value of E at the dg categories of perfect complexes of X, Z, and U. In the particular case where E is homotopy K-theory, this Gysin triangle yields a new proof of Quillen’s localization theorem, which avoids the use of devissage. As a first application, we prove that the value of E at a smooth scheme belongs to the smallest (thick) triangulated subcategory generated by the values of E at the smooth projective schemes. As a second application, we compute the additive invariants of relative cellular spaces in terms of the bases of the corresponding cells. Finally, as a third application, we construct explicit bridges relating motivic homotopy theory and mixed motives on the one side with noncommutative mixed motives on the other side. This leads to a comparison between different motivic Gysin triangles as well as to an etale descent result concerning noncommutative mixed motives with rational coefficients.
Date issued
2018-01
URI
http://hdl.handle.net/1721.1/116933
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Transactions of the American Mathematical Society
Publisher
American Mathematical Society (AMS)
Citation
Tabuada, Gonçalo, and Michel Van den Bergh. “The Gysin Triangle via Localization and A[superscript 1]-Homotopy Invariance.” Transactions of the American Mathematical Society, vol. 370, no. 1, Aug. 2017, pp. 421–46. © American Mathematical Society
Version: Final published version
ISSN
0002-9947
1088-6850

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.