Jacques Tits motivic measure

Detalhes bibliográficos
Autor(a) principal: Tabuada, Gonçalo
Data de Publicação: 2022
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/160062
Resumo: I am grateful to Michael Artin for enlightning discussions about Severi-Brauer varieties, to Marcello Bernardara for a stimulating discussion about the Amitsur’s conjecture, to Asher Auel for the references [8 , 20], and to the anonymous referees for their comments. I am also very grateful to the Institut des Hautes Études Scientifiques (IHÉS) and to the Max-Planck-Institut für Mathematik (MPIM) for their hospitality, where this work was finalized. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The author was partially supported by the Huawei-IHÉS research funds. Publisher Copyright: © 2021, The Author(s).
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spelling Jacques Tits motivic measureMathematics(all)I am grateful to Michael Artin for enlightning discussions about Severi-Brauer varieties, to Marcello Bernardara for a stimulating discussion about the Amitsur’s conjecture, to Asher Auel for the references [8 , 20], and to the anonymous referees for their comments. I am also very grateful to the Institut des Hautes Études Scientifiques (IHÉS) and to the Max-Planck-Institut für Mathematik (MPIM) for their hospitality, where this work was finalized. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The author was partially supported by the Huawei-IHÉS research funds. Publisher Copyright: © 2021, The Author(s).In this article we construct a new motivic measure called the Jacques Tits motivic measure. As a first main application, we prove that two Severi-Brauer varieties (or, more generally, two twisted Grassmannian varieties), associated to 2-torsion central simple algebras, have the same class in the Grothendieck ring of varieties if and only if they are isomorphic. In addition, we prove that if two Severi-Brauer varieties, associated to central simple algebras of period { 3 , 4 , 5 , 6 } , have the same class in the Grothendieck ring of varieties, then they are necessarily birational to each other. As a second main application, we prove that two quadric hypersurfaces (or, more generally, two involution varieties), associated to quadratic forms of dimension 6 or to quadratic forms of arbitrary dimension defined over a base field k with I3(k) = 0 , have the same class in the Grothendieck ring of varieties if and only if they are isomorphic. In addition, we prove that the latter main application also holds for products of quadric hypersurfaces.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesRUNTabuada, Gonçalo2023-11-16T22:10:40Z2022-042022-04-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article34application/pdfhttp://hdl.handle.net/10362/160062eng0025-5831PURE: 76310680https://doi.org/10.1007/s00208-021-02292-6info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T05:42:37Zoai:run.unl.pt:10362/160062Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:57:50.728397Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Jacques Tits motivic measure
title Jacques Tits motivic measure
spellingShingle Jacques Tits motivic measure
Tabuada, Gonçalo
Mathematics(all)
title_short Jacques Tits motivic measure
title_full Jacques Tits motivic measure
title_fullStr Jacques Tits motivic measure
title_full_unstemmed Jacques Tits motivic measure
title_sort Jacques Tits motivic measure
author Tabuada, Gonçalo
author_facet Tabuada, Gonçalo
author_role author
dc.contributor.none.fl_str_mv DM - Departamento de Matemática
CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Tabuada, Gonçalo
dc.subject.por.fl_str_mv Mathematics(all)
topic Mathematics(all)
description I am grateful to Michael Artin for enlightning discussions about Severi-Brauer varieties, to Marcello Bernardara for a stimulating discussion about the Amitsur’s conjecture, to Asher Auel for the references [8 , 20], and to the anonymous referees for their comments. I am also very grateful to the Institut des Hautes Études Scientifiques (IHÉS) and to the Max-Planck-Institut für Mathematik (MPIM) for their hospitality, where this work was finalized. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The author was partially supported by the Huawei-IHÉS research funds. Publisher Copyright: © 2021, The Author(s).
publishDate 2022
dc.date.none.fl_str_mv 2022-04
2022-04-01T00:00:00Z
2023-11-16T22:10:40Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/160062
url http://hdl.handle.net/10362/160062
dc.language.iso.fl_str_mv eng
language eng
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PURE: 76310680
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