Elmanto, Elden and Hoyois, Marc and Khan, Adeel A. and Sosnilo, Vladimir and Yakerson, Maria (2020) Framed transfers and motivic fundamental classes. JOURNAL OF TOPOLOGY, 13 (2). pp. 460-500. ISSN 1753-8416, 1753-8424
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We relate the recognition principle for infinite P1-loop spaces to the theory of motivic fundamental classes of Deglise, Jin and Khan. We first compare two kinds of transfers that are naturally defined on cohomology theories represented by motivic spectra: the framed transfers given by the recognition principle, which arise from Voevodsky's computation of the Nisnevish sheaf associated with An/(An-0), and the Gysin transfers defined via Verdier's deformation to the normal cone. We then introduce the category of finite R-correspondences for R a motivic ring spectrum, generalizing Voevodsky's category of finite correspondences and Calmes and Fasel's category of finite Milnor-Witt correspondences. Using the formalism of fundamental classes, we show that the natural functor from the category of framed correspondences to the category of R-module spectra factors through the category of finite R-correspondences.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | K-THEORY; OPERATIONS; CYCLES; 14F42 (primary); 14C17 (secondary) |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 22 Mar 2021 12:20 |
| Last Modified: | 22 Mar 2021 12:20 |
| URI: | https://pred.uni-regensburg.de/id/eprint/44489 |
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