Journal article 658 views
Framed motivic Gamma-spaces
Izvestiya: Mathematics, Volume: 87, Issue: 1, Pages: 1 - 28
Swansea University Author: Grigory Garkusha
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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...
Published in: | Izvestiya: Mathematics |
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ISSN: | 1064-5632 1468-4810 |
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Steklov Mathematical Institute
2023
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URI: | https://cronfa.swan.ac.uk/Record/cronfa60277 |
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2024-11-14T12:17:02Z |
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2023-09-04T15:48:51.6378176 v2 60277 2022-06-18 Framed motivic Gamma-spaces 7d3826fb9a28467bec426b8ffa3a60e0 0000-0001-9836-0714 Grigory Garkusha Grigory Garkusha true false 2022-06-18 MACS 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&jrnid=im&paperid=9246&option_lang=eng COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS 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 |
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Journal article |
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Izvestiya: Mathematics |
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87 |
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1 |
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1 |
publishDate |
2023 |
institution |
Swansea University |
issn |
1064-5632 1468-4810 |
doi_str_mv |
10.4213/im9246e |
publisher |
Steklov Mathematical Institute |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics |
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https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=9246&option_lang=eng |
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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 |
2023-01-01T08:17:43Z |
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1822389293642940416 |
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11.048561 |