Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces

Detalhes bibliográficos
Autor(a) principal: Tabuada, Gonçalo
Data de Publicação: 2020
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/145059
Resumo: The author is grateful to Joseph Ayoub for useful e-mail exchanges concerning the Schur-finiteness conjecture, and to the anonymous referee for her/his comments and for suggesting Remark 10. The author also would like to thank the Hausdorff Institute for Mathematics (HIM) in Bonn for its hospitality.
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spelling Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo SurfacesBass-finitenessconjecturedu Val del Pezzo surfacesnoncommutative algebraic geometrynoncommutative mixed motivesquadric fibrationsSchur-finiteness conjectureMathematics(all)The author is grateful to Joseph Ayoub for useful e-mail exchanges concerning the Schur-finiteness conjecture, and to the anonymous referee for her/his comments and for suggesting Remark 10. The author also would like to thank the Hausdorff Institute for Mathematics (HIM) in Bonn for its hospitality.Let Q → B be a quadric fibration and T → B a family of sextic du Val del Pezzo surfaces. Making use of the theory of noncommutative mixed motives, we establish a precise relation between the Schur-finiteness conjecture for Q, resp. for T, and the Schur-finiteness conjecture for B. As an application, we prove the Schur-finiteness conjecture for Q, resp. for T, when B is low-dimensional. Along the way, we obtain a proof of the Schur-finiteness conjecture for smooth complete intersections of two or three quadric hypersurfaces. Finally, we prove similar results for the Bass-finiteness conjecture.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesRUNTabuada, Gonçalo2022-10-26T22:09:25Z20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article16application/pdfhttp://hdl.handle.net/10362/145059eng1431-0635PURE: 32702254https://doi.org/10.25537/dm.2020v25.2339-2354info: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:RCAAP2024-03-11T05:25:11Zoai:run.unl.pt:10362/145059Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:51:53.872335Repositório 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 Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces
title Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces
spellingShingle Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces
Tabuada, Gonçalo
Bass-finiteness
conjecture
du Val del Pezzo surfaces
noncommutative algebraic geometry
noncommutative mixed motives
quadric fibrations
Schur-finiteness conjecture
Mathematics(all)
title_short Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces
title_full Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces
title_fullStr Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces
title_full_unstemmed Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces
title_sort Schur-Finiteness (and Bass-Finiteness) Conjecture for Quadric Fibrations and Families of Sextic du Val del Pezzo Surfaces
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 Bass-finiteness
conjecture
du Val del Pezzo surfaces
noncommutative algebraic geometry
noncommutative mixed motives
quadric fibrations
Schur-finiteness conjecture
Mathematics(all)
topic Bass-finiteness
conjecture
du Val del Pezzo surfaces
noncommutative algebraic geometry
noncommutative mixed motives
quadric fibrations
Schur-finiteness conjecture
Mathematics(all)
description The author is grateful to Joseph Ayoub for useful e-mail exchanges concerning the Schur-finiteness conjecture, and to the anonymous referee for her/his comments and for suggesting Remark 10. The author also would like to thank the Hausdorff Institute for Mathematics (HIM) in Bonn for its hospitality.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01T00:00:00Z
2022-10-26T22:09:25Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/145059
url http://hdl.handle.net/10362/145059
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1431-0635
PURE: 32702254
https://doi.org/10.25537/dm.2020v25.2339-2354
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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instacron:RCAAP
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