No Cover Image

Journal article 799 views 90 downloads

Group schemes and motivic spectra

Grigory Garkusha Orcid Logo

Israel Journal of Mathematics, Volume: 259, Pages: 727 - 758

Swansea University Author: Grigory Garkusha Orcid Logo

Check full text

DOI (Published version): 10.1007/s11856-023-2492-x

Abstract

By a theorem of Mandell, May, Schwede and Shipley the stable homotopy theory of classical S1-spectra is recovered from orthogonal spectra. In this paper general linear, special linear, symplectic, orthogonal and special orthogonal motivic spectra are introduced and studied. It is shown that stable h...

Full description

Published in: Israel Journal of Mathematics
ISSN: 0021-2172 1565-8511
Published: Springer Science and Business Media LLC 2024
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa59418
first_indexed 2022-02-18T21:14:39Z
last_indexed 2024-11-14T12:15:27Z
id cronfa59418
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2024-04-15T15:53:42.5195471</datestamp><bib-version>v2</bib-version><id>59418</id><entry>2022-02-16</entry><title>Group schemes and motivic spectra</title><swanseaauthors><author><sid>7d3826fb9a28467bec426b8ffa3a60e0</sid><ORCID>0000-0001-9836-0714</ORCID><firstname>Grigory</firstname><surname>Garkusha</surname><name>Grigory Garkusha</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2022-02-16</date><deptcode>MACS</deptcode><abstract>By a theorem of Mandell, May, Schwede and Shipley the stable homotopy theory of classical S1-spectra is recovered from orthogonal spectra. In this paper general linear, special linear, symplectic, orthogonal and special orthogonal motivic spectra are introduced and studied. It is shown that stable homotopy theory of motivic spectra is recovered from each of these types of spectra. An application is given for the localization functor C&#x2217;Fr : SHnis(k) &#x2192; SHnis(k) in the sense of that converts Morel&#x2013;Voevodsky stable motivic homotopy theory SH(k) into the equivalent local theory of framed bispectra.</abstract><type>Journal Article</type><journal>Israel Journal of Mathematics</journal><volume>259</volume><journalNumber/><paginationStart>727</paginationStart><paginationEnd>758</paginationEnd><publisher>Springer Science and Business Media LLC</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0021-2172</issnPrint><issnElectronic>1565-8511</issnElectronic><keywords/><publishedDay>15</publishedDay><publishedMonth>4</publishedMonth><publishedYear>2024</publishedYear><publishedDate>2024-04-15</publishedDate><doi>10.1007/s11856-023-2492-x</doi><url>http://dx.doi.org/10.1007/s11856-023-2492-x</url><notes>Preprint before peer-review in Israel Journal of Mathematics available via https://arxiv.org/abs/1812.01384v3</notes><college>COLLEGE NANME</college><department>Mathematics and Computer Science School</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>MACS</DepartmentCode><institution>Swansea University</institution><apcterm/><funders>EPSRC</funders><projectreference>EP/W012030/1</projectreference><lastEdited>2024-04-15T15:53:42.5195471</lastEdited><Created>2022-02-16T21:41:40.4055609</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Grigory</firstname><surname>Garkusha</surname><orcid>0000-0001-9836-0714</orcid><order>1</order></author></authors><documents><document><filename>59418__28174__0c58da6641124e4da31fac72bc65ebaf.pdf</filename><originalFilename>59418.pdf</originalFilename><uploaded>2023-07-25T14:41:37.0004541</uploaded><type>Output</type><contentLength>334393</contentLength><contentType>application/pdf</contentType><version>Version of Record</version><cronfaStatus>true</cronfaStatus><copyrightCorrect>false</copyrightCorrect></document></documents><OutputDurs/></rfc1807>
spelling 2024-04-15T15:53:42.5195471 v2 59418 2022-02-16 Group schemes and motivic spectra 7d3826fb9a28467bec426b8ffa3a60e0 0000-0001-9836-0714 Grigory Garkusha Grigory Garkusha true false 2022-02-16 MACS By a theorem of Mandell, May, Schwede and Shipley the stable homotopy theory of classical S1-spectra is recovered from orthogonal spectra. In this paper general linear, special linear, symplectic, orthogonal and special orthogonal motivic spectra are introduced and studied. It is shown that stable homotopy theory of motivic spectra is recovered from each of these types of spectra. An application is given for the localization functor C∗Fr : SHnis(k) → SHnis(k) in the sense of that converts Morel–Voevodsky stable motivic homotopy theory SH(k) into the equivalent local theory of framed bispectra. Journal Article Israel Journal of Mathematics 259 727 758 Springer Science and Business Media LLC 0021-2172 1565-8511 15 4 2024 2024-04-15 10.1007/s11856-023-2492-x http://dx.doi.org/10.1007/s11856-023-2492-x Preprint before peer-review in Israel Journal of Mathematics available via https://arxiv.org/abs/1812.01384v3 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University EPSRC EP/W012030/1 2024-04-15T15:53:42.5195471 2022-02-16T21:41:40.4055609 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Grigory Garkusha 0000-0001-9836-0714 1 59418__28174__0c58da6641124e4da31fac72bc65ebaf.pdf 59418.pdf 2023-07-25T14:41:37.0004541 Output 334393 application/pdf Version of Record true false
title Group schemes and motivic spectra
spellingShingle Group schemes and motivic spectra
Grigory Garkusha
title_short Group schemes and motivic spectra
title_full Group schemes and motivic spectra
title_fullStr Group schemes and motivic spectra
title_full_unstemmed Group schemes and motivic spectra
title_sort Group schemes and motivic spectra
author_id_str_mv 7d3826fb9a28467bec426b8ffa3a60e0
author_id_fullname_str_mv 7d3826fb9a28467bec426b8ffa3a60e0_***_Grigory Garkusha
author Grigory Garkusha
author2 Grigory Garkusha
format Journal article
container_title Israel Journal of Mathematics
container_volume 259
container_start_page 727
publishDate 2024
institution Swansea University
issn 0021-2172
1565-8511
doi_str_mv 10.1007/s11856-023-2492-x
publisher Springer Science and Business Media LLC
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/10.1007/s11856-023-2492-x
document_store_str 1
active_str 0
description By a theorem of Mandell, May, Schwede and Shipley the stable homotopy theory of classical S1-spectra is recovered from orthogonal spectra. In this paper general linear, special linear, symplectic, orthogonal and special orthogonal motivic spectra are introduced and studied. It is shown that stable homotopy theory of motivic spectra is recovered from each of these types of spectra. An application is given for the localization functor C∗Fr : SHnis(k) → SHnis(k) in the sense of that converts Morel–Voevodsky stable motivic homotopy theory SH(k) into the equivalent local theory of framed bispectra.
published_date 2024-04-15T05:13:36Z
_version_ 1821381142754885632
score 11.04748

Similar Items