Strong A1${\mathbb {A}}^1$‐invariance of A1${\mathbb {A}}^1$‐connected components of reductive algebraic groups

We show that the sheaf of A1${\mathbb {A}}^1$‐connected components of a reductive algebraic group over a perfect field is strongly A1${\mathbb {A}}^1$‐invariant. As a consequence, torsors under such groups give rise to A1${\mathbb {A}}^1$‐fiber sequences. We also show that sections of A1${\mathbb {A...

Full description

Saved in:
Bibliographic Details
Published in:Journal of topology 2023-06, Vol.16 (2), p.634-649
Main Authors: Balwe, Chetan, Hogadi, Amit, Sawant, Anand
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c778-5a6e5bbec0df7d34efbdef3204e0c61013ea20ad6b78aef650e99dbf96dfe1233
container_end_page 649
container_issue 2
container_start_page 634
container_title Journal of topology
container_volume 16
creator Balwe, Chetan
Hogadi, Amit
Sawant, Anand
description We show that the sheaf of A1${\mathbb {A}}^1$‐connected components of a reductive algebraic group over a perfect field is strongly A1${\mathbb {A}}^1$‐invariant. As a consequence, torsors under such groups give rise to A1${\mathbb {A}}^1$‐fiber sequences. We also show that sections of A1${\mathbb {A}}^1$‐connected components of anisotropic, semisimple, simply connected algebraic groups over an arbitrary field agree with their R$R$‐equivalence classes, thereby removing the perfectness assumption in the previously known results about the characterization of isotropy in terms of affine homotopy invariance of Nisnevich locally trivial torsors.
doi_str_mv 10.1112/topo.12298
format article
fullrecord <record><control><sourceid>wiley_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1112_topo_12298</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>TOPO12298</sourcerecordid><originalsourceid>FETCH-LOGICAL-c778-5a6e5bbec0df7d34efbdef3204e0c61013ea20ad6b78aef650e99dbf96dfe1233</originalsourceid><addsrcrecordid>eNp90M1Kw0AQwPFFFKzVi0-QQ09C6s4m2STHUvyCQgVzFMN-zNZIuxt200opBR_BZ_RJtFa86Wnm8Js5_Ak5BzoEAHbZudYNgbGyOCA9yLMkLlKWHv7uwI_JSQgvlHJGE94j4aHzzs6iEQw2jwvRPUsZbUbb7RMMPt7eG7sSvhFWYeTMH0Y5a1F1qCPlFq2zaLuw0x71UnXNCiMxn6H0olHRzLtlG07JkRHzgGc_s0-q66tqfBtPpjd349EkVnlexJngmEmJimqT6yRFIzWahNEUqeJAIUHBqNBc5oVAwzOKZamlKbk2CCxJ-uRi_1Z5F4JHU7e-WQi_roHWu1r1rlb9XesLwx6_NnNc_yPrano_3d98Ag_pcgI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Strong A1${\mathbb {A}}^1$‐invariance of A1${\mathbb {A}}^1$‐connected components of reductive algebraic groups</title><source>Wiley</source><creator>Balwe, Chetan ; Hogadi, Amit ; Sawant, Anand</creator><creatorcontrib>Balwe, Chetan ; Hogadi, Amit ; Sawant, Anand</creatorcontrib><description>We show that the sheaf of A1${\mathbb {A}}^1$‐connected components of a reductive algebraic group over a perfect field is strongly A1${\mathbb {A}}^1$‐invariant. As a consequence, torsors under such groups give rise to A1${\mathbb {A}}^1$‐fiber sequences. We also show that sections of A1${\mathbb {A}}^1$‐connected components of anisotropic, semisimple, simply connected algebraic groups over an arbitrary field agree with their R$R$‐equivalence classes, thereby removing the perfectness assumption in the previously known results about the characterization of isotropy in terms of affine homotopy invariance of Nisnevich locally trivial torsors.</description><identifier>ISSN: 1753-8416</identifier><identifier>EISSN: 1753-8424</identifier><identifier>DOI: 10.1112/topo.12298</identifier><language>eng</language><ispartof>Journal of topology, 2023-06, Vol.16 (2), p.634-649</ispartof><rights>2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c778-5a6e5bbec0df7d34efbdef3204e0c61013ea20ad6b78aef650e99dbf96dfe1233</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Balwe, Chetan</creatorcontrib><creatorcontrib>Hogadi, Amit</creatorcontrib><creatorcontrib>Sawant, Anand</creatorcontrib><title>Strong A1${\mathbb {A}}^1$‐invariance of A1${\mathbb {A}}^1$‐connected components of reductive algebraic groups</title><title>Journal of topology</title><description>We show that the sheaf of A1${\mathbb {A}}^1$‐connected components of a reductive algebraic group over a perfect field is strongly A1${\mathbb {A}}^1$‐invariant. As a consequence, torsors under such groups give rise to A1${\mathbb {A}}^1$‐fiber sequences. We also show that sections of A1${\mathbb {A}}^1$‐connected components of anisotropic, semisimple, simply connected algebraic groups over an arbitrary field agree with their R$R$‐equivalence classes, thereby removing the perfectness assumption in the previously known results about the characterization of isotropy in terms of affine homotopy invariance of Nisnevich locally trivial torsors.</description><issn>1753-8416</issn><issn>1753-8424</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp90M1Kw0AQwPFFFKzVi0-QQ09C6s4m2STHUvyCQgVzFMN-zNZIuxt200opBR_BZ_RJtFa86Wnm8Js5_Ak5BzoEAHbZudYNgbGyOCA9yLMkLlKWHv7uwI_JSQgvlHJGE94j4aHzzs6iEQw2jwvRPUsZbUbb7RMMPt7eG7sSvhFWYeTMH0Y5a1F1qCPlFq2zaLuw0x71UnXNCiMxn6H0olHRzLtlG07JkRHzgGc_s0-q66tqfBtPpjd349EkVnlexJngmEmJimqT6yRFIzWahNEUqeJAIUHBqNBc5oVAwzOKZamlKbk2CCxJ-uRi_1Z5F4JHU7e-WQi_roHWu1r1rlb9XesLwx6_NnNc_yPrano_3d98Ag_pcgI</recordid><startdate>202306</startdate><enddate>202306</enddate><creator>Balwe, Chetan</creator><creator>Hogadi, Amit</creator><creator>Sawant, Anand</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>202306</creationdate><title>Strong A1${\mathbb {A}}^1$‐invariance of A1${\mathbb {A}}^1$‐connected components of reductive algebraic groups</title><author>Balwe, Chetan ; Hogadi, Amit ; Sawant, Anand</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c778-5a6e5bbec0df7d34efbdef3204e0c61013ea20ad6b78aef650e99dbf96dfe1233</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Balwe, Chetan</creatorcontrib><creatorcontrib>Hogadi, Amit</creatorcontrib><creatorcontrib>Sawant, Anand</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of topology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Balwe, Chetan</au><au>Hogadi, Amit</au><au>Sawant, Anand</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Strong A1${\mathbb {A}}^1$‐invariance of A1${\mathbb {A}}^1$‐connected components of reductive algebraic groups</atitle><jtitle>Journal of topology</jtitle><date>2023-06</date><risdate>2023</risdate><volume>16</volume><issue>2</issue><spage>634</spage><epage>649</epage><pages>634-649</pages><issn>1753-8416</issn><eissn>1753-8424</eissn><abstract>We show that the sheaf of A1${\mathbb {A}}^1$‐connected components of a reductive algebraic group over a perfect field is strongly A1${\mathbb {A}}^1$‐invariant. As a consequence, torsors under such groups give rise to A1${\mathbb {A}}^1$‐fiber sequences. We also show that sections of A1${\mathbb {A}}^1$‐connected components of anisotropic, semisimple, simply connected algebraic groups over an arbitrary field agree with their R$R$‐equivalence classes, thereby removing the perfectness assumption in the previously known results about the characterization of isotropy in terms of affine homotopy invariance of Nisnevich locally trivial torsors.</abstract><doi>10.1112/topo.12298</doi><tpages>16</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1753-8416
ispartof Journal of topology, 2023-06, Vol.16 (2), p.634-649
issn 1753-8416
1753-8424
language eng
recordid cdi_crossref_primary_10_1112_topo_12298
source Wiley
title Strong A1${\mathbb {A}}^1$‐invariance of A1${\mathbb {A}}^1$‐connected components of reductive algebraic groups
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T16%3A12%3A03IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wiley_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Strong%20A1$%7B%5Cmathbb%20%7BA%7D%7D%5E1$%E2%80%90invariance%20of%20A1$%7B%5Cmathbb%20%7BA%7D%7D%5E1$%E2%80%90connected%20components%20of%20reductive%20algebraic%20groups&rft.jtitle=Journal%20of%20topology&rft.au=Balwe,%20Chetan&rft.date=2023-06&rft.volume=16&rft.issue=2&rft.spage=634&rft.epage=649&rft.pages=634-649&rft.issn=1753-8416&rft.eissn=1753-8424&rft_id=info:doi/10.1112/topo.12298&rft_dat=%3Cwiley_cross%3ETOPO12298%3C/wiley_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c778-5a6e5bbec0df7d34efbdef3204e0c61013ea20ad6b78aef650e99dbf96dfe1233%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true