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Homotopy invariant presheaves with framed transfers
,
Ivan Panin
Cambridge Journal of Mathematics, Volume: 8, Issue: 1, Pages: 1 - 94
Swansea University Author:
Grigory Garkusha
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DOI (Published version): 10.4310/cjm.2020.v8.n1.a1
Abstract
The category of framed correspondences F r∗(k), framed presheaves and framed sheaves were invented by Voevodsky in his unpublished notes [20]. Based on the notes [20] a new approach to the classical Morel–Voevodsky motivic stable homotopy theory was developed in [8]. This approach converts the class...
| Published in: | Cambridge Journal of Mathematics |
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| ISSN: | 2168-0930 2168-0949 |
| Published: |
International Press of Boston
2020
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa52799 |
| Abstract: |
The category of framed correspondences F r∗(k), framed presheaves and framed sheaves were invented by Voevodsky in his unpublished notes [20]. Based on the notes [20] a new approach to the classical Morel–Voevodsky motivic stable homotopy theory was developed in [8]. This approach converts the classical motivic stable homotopy theory into an equivalent local theory of framed bispectra. The main result of the paper is the core of the theory of framed bispectra. It states that for any homotopy invariant quasi-stable radditive framed presheaf of Abelian groups F, the associated Nisnevich sheaf Fnis is strictly homotopy invariant and quasi-stable whenever the base field k is infinite perfect of characteristic different from 2. |
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| Keywords: |
motivic homotopy theory, framed presheaves |
| College: |
Faculty of Science and Engineering |
| Funders: |
The authors acknowledge support by the RCN Frontier Research Group Project no. 250399 “Motivic Hopf Equations”. |
| Issue: |
1 |
| Start Page: |
1 |
| End Page: |
94 |