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http://hdl.handle.net/1942/26283
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DC Field | Value | Language |
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dc.contributor.author | Tabuada, Goncalo | - |
dc.contributor.author | VAN DEN BERGH, Michel | - |
dc.date.accessioned | 2018-07-10T10:40:03Z | - |
dc.date.available | 2018-07-10T10:40:03Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 370(1), p. 421-446 | - |
dc.identifier.issn | 0002-9947 | - |
dc.identifier.uri | http://hdl.handle.net/1942/26283 | - |
dc.description.abstract | Let X be a smooth scheme, Z a smooth closed subscheme, and U the open complement. Given any localizing and A(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. | - |
dc.description.sponsorship | The first author was partially supported by the NSF CAREER Award #1350472 and by the Portuguese Foundation for Science and Technology grant PEst-OE/MAT/UI0297/2014. | - |
dc.language.iso | en | - |
dc.publisher | AMER MATHEMATICAL SOC | - |
dc.rights | (C) 2017 American Mathematical society | - |
dc.subject.other | Localization; A(1)-homotopy; dg category; algebraic K-theory; periodic cyclic homology; algebraic spaces; motivic homotopy theory; (noncommutative) mixed motives; Nisnevich and etale descent; relative cellular spaces; noncommutative algebraic geometry | - |
dc.subject.other | localization; A(1)-homotopy; dg category; algebraic K-theory; periodic cyclic homology; algebraic spaces; motivic homotopy theory; (noncommutative) mixed motives; Nisnevich and etale descent; relative cellular spaces; noncommutative algebraic geometry | - |
dc.title | The Gysin triangle via localization and A(1)-homotopy invariance | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 446 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 421 | - |
dc.identifier.volume | 370 | - |
local.format.pages | 26 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | [Tabuada, Goncalo] MIT, Dept Math, Cambridge, MA 02139 USA. [Tabuada, Goncalo] Univ Nova Lsiboa, Fac Ciencias & Tecnol, Dept Matemat, P-2829516 Quinta Da Torre, Caparica, Portugal. [Tabuada, Goncalo] Univ Nova Lsiboa, Fac Ciencias & Tecnol, Ctr Matemat & Aplicacoes, P-2829516 Quinta Da Torre, Caparica, Portugal. [Van den Bergh, Michel] Univ Hasselt, Dept WNI, B-3590 Diepenbeek, Belgium. | - |
local.publisher.place | PROVIDENCE | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.1090/tran/6956 | - |
dc.identifier.isi | 000414149300014 | - |
item.contributor | Tabuada, Goncalo | - |
item.contributor | VAN DEN BERGH, Michel | - |
item.fullcitation | Tabuada, Goncalo & VAN DEN BERGH, Michel (2018) The Gysin triangle via localization and A(1)-homotopy invariance. In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 370(1), p. 421-446. | - |
item.accessRights | Open Access | - |
item.fulltext | With Fulltext | - |
item.validation | ecoom 2018 | - |
crisitem.journal.issn | 0002-9947 | - |
crisitem.journal.eissn | 1088-6850 | - |
Appears in Collections: | Research publications |
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Bergh.pdf Restricted Access | Published version | 428.04 kB | Adobe PDF | View/Open Request a copy |
1510.04677.pdf | Non Peer-reviewed author version | 406.81 kB | Adobe PDF | View/Open |
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