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Correspondences and stable homotopy theory

Grigory Garkusha Orcid Logo

Transactions of the London Mathematical Society, Volume: 10, Issue: 1, Pages: 124 - 155

Swansea University Author: Grigory Garkusha Orcid Logo

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DOI (Published version): 10.1112/tlm3.12056

Abstract

A general method of producing correspondences andspectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra is recovered from modulesover a commutative symmetric ring spectrum defined interms of framed correspondences over a...

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Published in: Transactions of the London Mathematical Society
ISSN: 2052-4986 2052-4986
Published: Wiley 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa64111
first_indexed 2023-09-29T11:47:29Z
last_indexed 2024-11-25T14:13:28Z
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spelling 2023-10-02T12:21:05.4654666 v2 64111 2023-08-23 Correspondences and stable homotopy theory 7d3826fb9a28467bec426b8ffa3a60e0 0000-0001-9836-0714 Grigory Garkusha Grigory Garkusha true false 2023-08-23 MACS A general method of producing correspondences andspectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra is recovered from modulesover a commutative symmetric ring spectrum defined interms of framed correspondences over an algebraically closed field. Another application recovers stable motivic homotopy theory () from spectral modules over associated spectral categories. Journal Article Transactions of the London Mathematical Society 10 1 124 155 Wiley 2052-4986 2052-4986 1 12 2023 2023-12-01 10.1112/tlm3.12056 http://dx.doi.org/10.1112/tlm3.12056 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University SU College/Department paid the OA fee EPSRC, EP/W012030/1 2023-10-02T12:21:05.4654666 2023-08-23T11:50:59.1690552 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Grigory Garkusha 0000-0001-9836-0714 1 64111__28675__46139cb85d1c4457936566afe205d804.pdf 64111.VOR.pdf 2023-10-02T12:19:00.7552208 Output 435387 application/pdf Version of Record true © 2023 The Authors. Transactions of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. true eng https://creativecommons.org/licenses/by/4.0/
title Correspondences and stable homotopy theory
spellingShingle Correspondences and stable homotopy theory
Grigory Garkusha
title_short Correspondences and stable homotopy theory
title_full Correspondences and stable homotopy theory
title_fullStr Correspondences and stable homotopy theory
title_full_unstemmed Correspondences and stable homotopy theory
title_sort Correspondences and stable homotopy theory
author_id_str_mv 7d3826fb9a28467bec426b8ffa3a60e0
author_id_fullname_str_mv 7d3826fb9a28467bec426b8ffa3a60e0_***_Grigory Garkusha
author Grigory Garkusha
author2 Grigory Garkusha
format Journal article
container_title Transactions of the London Mathematical Society
container_volume 10
container_issue 1
container_start_page 124
publishDate 2023
institution Swansea University
issn 2052-4986
2052-4986
doi_str_mv 10.1112/tlm3.12056
publisher Wiley
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 http://dx.doi.org/10.1112/tlm3.12056
document_store_str 1
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description A general method of producing correspondences andspectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra is recovered from modulesover a commutative symmetric ring spectrum defined interms of framed correspondences over an algebraically closed field. Another application recovers stable motivic homotopy theory () from spectral modules over associated spectral categories.
published_date 2023-12-01T08:23:36Z
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score 11.047501

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