Publicação
Jacques Tits motivic measure
| dc.contributor.author | Tabuada, Gonçalo | |
| dc.contributor.institution | DM - Departamento de Matemática | |
| dc.contributor.institution | CMA - Centro de Matemática e Aplicações | |
| dc.contributor.pbl | Springer New York | |
| dc.date.accessioned | 2023-11-16T22:10:40Z | |
| dc.date.available | 2023-11-16T22:10:40Z | |
| dc.date.issued | 2022-04 | |
| dc.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). | |
| dc.description.abstract | 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. | en |
| dc.description.version | publishersversion | |
| dc.description.version | published | |
| dc.format.extent | 34 | |
| dc.format.extent | 561408 | |
| dc.identifier.doi | 10.1007/s00208-021-02292-6 | |
| dc.identifier.issn | 0025-5831 | |
| dc.identifier.other | PURE: 76310680 | |
| dc.identifier.other | PURE UUID: 1b8bb0de-e3a3-434e-95fd-5eacd640c0f4 | |
| dc.identifier.other | Scopus: 85118542678 | |
| dc.identifier.other | WOS: 000715022100001 | |
| dc.identifier.uri | http://hdl.handle.net/10362/160062 | |
| dc.identifier.url | https://www.scopus.com/pages/publications/85118542678 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.relation | Funding Information: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT | |
| dc.subject | General Mathematics | |
| dc.title | Jacques Tits motivic measure | en |
| dc.type | journal article | |
| degois.publication.firstPage | 1245 | |
| degois.publication.issue | 3-4 | |
| degois.publication.lastPage | 1278 | |
| degois.publication.title | Mathematische Annalen | |
| degois.publication.volume | 382 | |
| dspace.entity.type | Publication | |
| rcaap.rights | openAccess |
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