Irrationality of generic cubic threefold ...
Document type :
Article dans une revue scientifique: Article original
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Title :
Irrationality of generic cubic threefold via Weil's conjectures
Author(s) :
Markushevich, Dimitri [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Roulleau, Xavier [Auteur]
Institut de Mathématiques de Marseille [I2M]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Roulleau, Xavier [Auteur]
Institut de Mathématiques de Marseille [I2M]
Journal title :
Communications in Contemporary Mathematics
Pages :
1750078
Publisher :
World Scientific Publishing
Publication date :
2018-10-14
ISSN :
0219-1997
English keyword(s) :
Cubic hypersurfaces
Weil's conjectures
finite fields
Fano varieties
intermediate Jacobian
irrational varieties
Weil's conjectures
finite fields
Fano varieties
intermediate Jacobian
irrational varieties
HAL domain(s) :
Mathématiques [math]/Géométrie algébrique [math.AG]
English abstract : [en]
An arithmetic method of proving the irrationality of smooth projective 3-folds is described, using reduction modulo p. It is illustrated by an application to a cubic threefold, for which the hypothesis that its intermediate ...
Show more >An arithmetic method of proving the irrationality of smooth projective 3-folds is described, using reduction modulo p. It is illustrated by an application to a cubic threefold, for which the hypothesis that its intermediate Jacobian is isomorphic to the Jacobian of a curve is contradicted by reducing modulo 3 and counting points over appropriate extensions of F-3. As a spin-off, it is shown that the 5-dimensional Prym varieties arising as intermediate Jacobians of certain cubic 3-folds have the maximal number of points over F-q which attains Perret's and Weil's upper bounds.Show less >
Show more >An arithmetic method of proving the irrationality of smooth projective 3-folds is described, using reduction modulo p. It is illustrated by an application to a cubic threefold, for which the hypothesis that its intermediate Jacobian is isomorphic to the Jacobian of a curve is contradicted by reducing modulo 3 and counting points over appropriate extensions of F-3. As a spin-off, it is shown that the 5-dimensional Prym varieties arising as intermediate Jacobians of certain cubic 3-folds have the maximal number of points over F-q which attains Perret's and Weil's upper bounds.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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Submission date :
2025-01-24T17:16:04Z