Titre :

Irrationality of generic cubic threefold via Weil's conjectures

Auteur(s) :

Markushevich, Dimitri [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Roulleau, Xavier [Auteur]
Institut de Mathématiques de Marseille [I2M]

Titre de la revue :

Communications in Contemporary Mathematics

Pagination :

1750078

Éditeur :

World Scientific Publishing

Date de publication :

2018-10-14

ISSN :

0219-1997

Mot(s)-clé(s) en anglais :

Cubic hypersurfaces
Weil's conjectures
finite fields
Fano varieties
intermediate Jacobian
irrational varieties

Discipline(s) HAL :

Mathématiques [math]/Géométrie algébrique [math.AG]

Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T17:16:04Z