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Homotopy invariant presheaves with framed transfers

Grigory Garkusha Orcid Logo, Ivan Panin

Cambridge Journal of Mathematics, Volume: 8, Issue: 1, Pages: 1 - 94

Swansea University Author: Grigory Garkusha Orcid Logo

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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The category of framed correspondences F r∗(k), framed presheaves and framed sheaves were invented by Voevodsky in his unpublished notes [20].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...

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Published in: Cambridge Journal of Mathematics
ISSN: 2168-0930 2168-0949
Published: International Press of Boston 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa52799
first_indexed 2019-11-20T13:14:58Z
last_indexed 2025-04-10T05:36:02Z
id cronfa52799
recordtype SURis
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spelling 2025-04-09T15:53:37.1400606 v2 52799 2019-11-20 Homotopy invariant presheaves with framed transfers 7d3826fb9a28467bec426b8ffa3a60e0 0000-0001-9836-0714 Grigory Garkusha Grigory Garkusha true false 2019-11-20 MACS The category of framed correspondences F r∗(k), framed presheaves and framed sheaves were invented by Voevodsky in his unpublished notes [20].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. Journal Article Cambridge Journal of Mathematics 8 1 1 94 International Press of Boston 2168-0930 2168-0949 motivic homotopy theory, framed presheaves 25 2 2020 2020-02-25 10.4310/cjm.2020.v8.n1.a1 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University The authors acknowledge support by the RCN Frontier Research Group Project no. 250399 “Motivic Hopf Equations”. 2025-04-09T15:53:37.1400606 2019-11-20T11:41:21.6041508 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Grigory Garkusha 0000-0001-9836-0714 1 Ivan Panin 2
title Homotopy invariant presheaves with framed transfers
spellingShingle Homotopy invariant presheaves with framed transfers
Grigory Garkusha
title_short Homotopy invariant presheaves with framed transfers
title_full Homotopy invariant presheaves with framed transfers
title_fullStr Homotopy invariant presheaves with framed transfers
title_full_unstemmed Homotopy invariant presheaves with framed transfers
title_sort Homotopy invariant presheaves with framed transfers
author_id_str_mv 7d3826fb9a28467bec426b8ffa3a60e0
author_id_fullname_str_mv 7d3826fb9a28467bec426b8ffa3a60e0_***_Grigory Garkusha
author Grigory Garkusha
author2 Grigory Garkusha
Ivan Panin
format Journal article
container_title Cambridge Journal of Mathematics
container_volume 8
container_issue 1
container_start_page 1
publishDate 2020
institution Swansea University
issn 2168-0930
2168-0949
doi_str_mv 10.4310/cjm.2020.v8.n1.a1
publisher International Press of Boston
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 0
active_str 0
description 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.
published_date 2020-02-25T04:43:29Z
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score 11.089572

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