A note on grothendieck’s standard conjectures of type C+ and D

Detalhes bibliográficos
Autor(a) principal: Tabuada, Gonçalo
Data de Publicação: 2018
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/162697
Resumo: 1350472 and by the Portuguese Foundation for Science and Technology grant PEst-OE/MAT/UI0297/2014. 1The standard conjecture of type C+ is also usually known as the s∑ign conjecture. If the even Künneth projector is algebraic, then the odd Künneth projector πX− := iπX2i+1 is also algebraic. 2When X is quasi-projective this dg enhancement is unique; see Lunts–Orlov [16, Thm. 2.12]. Publisher Copyright: © 2018 American Mathematical Society.
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spelling A note on grothendieck’s standard conjectures of type C+ and DMathematics(all)Applied Mathematics1350472 and by the Portuguese Foundation for Science and Technology grant PEst-OE/MAT/UI0297/2014. 1The standard conjecture of type C+ is also usually known as the s∑ign conjecture. If the even Künneth projector is algebraic, then the odd Künneth projector πX− := iπX2i+1 is also algebraic. 2When X is quasi-projective this dg enhancement is unique; see Lunts–Orlov [16, Thm. 2.12]. Publisher Copyright: © 2018 American Mathematical Society.Grothendieck conjectured in the sixties that the even Künneth projector (with respect to a Weil cohomology theory) is algebraic and that the homological equivalence relation on algebraic cycles coincides with the numerical equivalence relation. In this note we extend these celebrated conjectures from smooth projective schemes to the broad setting of smooth proper dg categories. As an application, we prove that Grothendieck’s conjectures are invariant under homological projective duality. This leads to a proof of Grothendieck’s original conjectures in the case of intersections of quadrics and linear sections of determinantal varieties. Along the way, we also prove the case of quadric fibrations and intersections of bilinear divisors.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNTabuada, Gonçalo2024-01-24T15:15:07Z20182018-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article11application/pdfhttp://hdl.handle.net/10362/162697eng0002-9939PURE: 76337476https://doi.org/10.1090/proc/13955info: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:RCAAP2024-03-11T05:45:38Zoai:run.unl.pt:10362/162697Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:59:01.406831Repositório 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 A note on grothendieck’s standard conjectures of type C+ and D
title A note on grothendieck’s standard conjectures of type C+ and D
spellingShingle A note on grothendieck’s standard conjectures of type C+ and D
Tabuada, Gonçalo
Mathematics(all)
Applied Mathematics
title_short A note on grothendieck’s standard conjectures of type C+ and D
title_full A note on grothendieck’s standard conjectures of type C+ and D
title_fullStr A note on grothendieck’s standard conjectures of type C+ and D
title_full_unstemmed A note on grothendieck’s standard conjectures of type C+ and D
title_sort A note on grothendieck’s standard conjectures of type C+ and D
author Tabuada, Gonçalo
author_facet Tabuada, Gonçalo
author_role author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Tabuada, Gonçalo
dc.subject.por.fl_str_mv Mathematics(all)
Applied Mathematics
topic Mathematics(all)
Applied Mathematics
description 1350472 and by the Portuguese Foundation for Science and Technology grant PEst-OE/MAT/UI0297/2014. 1The standard conjecture of type C+ is also usually known as the s∑ign conjecture. If the even Künneth projector is algebraic, then the odd Künneth projector πX− := iπX2i+1 is also algebraic. 2When X is quasi-projective this dg enhancement is unique; see Lunts–Orlov [16, Thm. 2.12]. Publisher Copyright: © 2018 American Mathematical Society.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01T00:00:00Z
2024-01-24T15:15:07Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/162697
url http://hdl.handle.net/10362/162697
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0002-9939
PURE: 76337476
https://doi.org/10.1090/proc/13955
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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