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Framed motivic Gamma-spaces

Grigory Garkusha Orcid Logo, Ivan Panin, Paul Arne Ostvaer

Izvestiya: Mathematics, Volume: 87, Issue: 1, Pages: 1 - 28

Swansea University Author: Grigory Garkusha Orcid Logo

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DOI (Published version): 10.4213/im9246e

Abstract

We combine several mini miracles to achieve an elementary understanding of infinite loop spaces and very effective spectra in the algebro-geometric setting of motivic homotopy theory. Our approach combines Γ-spaces and Voevodsky’s framed correspondences into the concept of framed motivic Γ-spaces; t...

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Published in: Izvestiya: Mathematics
ISSN: 1064-5632 1468-4810
Published: Steklov Mathematical Institute 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa60277
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first_indexed 2022-06-18T15:58:27Z
last_indexed 2023-03-14T04:19:43Z
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spelling v2 60277 2022-06-18 Framed motivic Gamma-spaces 7d3826fb9a28467bec426b8ffa3a60e0 0000-0001-9836-0714 Grigory Garkusha Grigory Garkusha true false 2022-06-18 SMA We combine several mini miracles to achieve an elementary understanding of infinite loop spaces and very effective spectra in the algebro-geometric setting of motivic homotopy theory. Our approach combines Γ-spaces and Voevodsky’s framed correspondences into the concept of framed motivic Γ-spaces; these are continuous or enriched functors of two variables that take values in framed motivic spaces. We craft proofs of our main results by imposing further axioms on framed motivic Γ-spaces such as a Segal condition for simplicial Nisnevich sheaves, cancellation, A1- and σ-invariance, Nisnevich excision, Suslin contractibility, and grouplikeness. This adds to the discussion in the literature on coexisting points of view on the A1-homotopy theory of algebraic varieties. Journal Article Izvestiya: Mathematics 87 1 1 28 Steklov Mathematical Institute 1064-5632 1468-4810 Framed correspondences, Γ-spaces, motivic spaces, framed motivic Γ-spaces, connective and very effective motivic spectra, infinite motivic loop spaces. 1 1 2023 2023-01-01 10.4213/im9246e https://www.mathnet.ru/php/archive.phtml?wshow=paper&amp;jrnid=im&amp;paperid=9246&amp;option_lang=eng COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2023-09-04T15:48:51.6378176 2022-06-18T16:44:55.9643235 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Grigory Garkusha 0000-0001-9836-0714 1 Ivan Panin 2 Paul Arne Ostvaer 3
title Framed motivic Gamma-spaces
spellingShingle Framed motivic Gamma-spaces
Grigory Garkusha
title_short Framed motivic Gamma-spaces
title_full Framed motivic Gamma-spaces
title_fullStr Framed motivic Gamma-spaces
title_full_unstemmed Framed motivic Gamma-spaces
title_sort Framed motivic Gamma-spaces
author_id_str_mv 7d3826fb9a28467bec426b8ffa3a60e0
author_id_fullname_str_mv 7d3826fb9a28467bec426b8ffa3a60e0_***_Grigory Garkusha
author Grigory Garkusha
author2 Grigory Garkusha
Ivan Panin
Paul Arne Ostvaer
format Journal article
container_title Izvestiya: Mathematics
container_volume 87
container_issue 1
container_start_page 1
publishDate 2023
institution Swansea University
issn 1064-5632
1468-4810
doi_str_mv 10.4213/im9246e
publisher Steklov Mathematical Institute
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
url https://www.mathnet.ru/php/archive.phtml?wshow=paper&amp;jrnid=im&amp;paperid=9246&amp;option_lang=eng
document_store_str 0
active_str 0
description We combine several mini miracles to achieve an elementary understanding of infinite loop spaces and very effective spectra in the algebro-geometric setting of motivic homotopy theory. Our approach combines Γ-spaces and Voevodsky’s framed correspondences into the concept of framed motivic Γ-spaces; these are continuous or enriched functors of two variables that take values in framed motivic spaces. We craft proofs of our main results by imposing further axioms on framed motivic Γ-spaces such as a Segal condition for simplicial Nisnevich sheaves, cancellation, A1- and σ-invariance, Nisnevich excision, Suslin contractibility, and grouplikeness. This adds to the discussion in the literature on coexisting points of view on the A1-homotopy theory of algebraic varieties.
published_date 2023-01-01T15:48:53Z
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score 11.014067

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