Publicação
A note on grothendieck’s standard conjectures of type C+ and D
| Resumo: | 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. |
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| Autores principais: | Tabuada, Gonçalo |
| Assunto: | General Mathematics Applied Mathematics |
| Ano: | 2018 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Nova de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório Institucional da UNL |
| Resumo: | 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. |
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