Projective geometry for blueprints

López Peña, Javier; Lorscheid, Oliver

doi:10.1016/j.crma.2012.05.001

Algebra/Algebraic Geometry

Projective geometry for blueprints
[Geometrie projective pour les canevas bleus]

Présenté par : Christophe Soulé

López Peña, Javier ¹ ; Lorscheid, Oliver ²

¹ Department of Mathematics, University College London, 25 Gower Street, London WC1E 6BT, United Kingdom
² Department of Mathematics, University of Wuppertal, Gaußstr. 20, 42097 Wuppertal, Germany

Comptes Rendus. Mathématique, Tome 350 (2012) no. 9-10, pp. 455-458.

Résumé
Abstract

Dans cette Note, nous généralisons la Proj-construction des schémas usuels aux schémas bleus. Cela entraine la définition dʼespace projectif et de variétés projectives sur un canevas bleu. En particulier, il est possible de descendre une sous-variété fermée dʼun espace projectif en un $F_{1}$ -modèle canonique. Nous discutons cela dans le cas de la Grassmannienne $Gr (2, 4)$ .

In this Note, we generalize the Proj-construction from usual schemes to blue schemes. This yields the definition of projective space and projective varieties over a blueprint. In particular, it is possible to descend closed subvarieties of a projective space to a canonical $F_{1}$ -model. We discuss this in case of the Grassmannian $Gr (2, 4)$ .

Reçu le : 2012-03-08
Accepté le : 2012-04-27
Publié le : 2012-05-01

DOI : 10.1016/j.crma.2012.05.001

Affiliations des auteurs :

López Peña, Javier ¹ ; Lorscheid, Oliver ²

¹ Department of Mathematics, University College London, 25 Gower Street, London WC1E 6BT, United Kingdom
² Department of Mathematics, University of Wuppertal, Gaußstr. 20, 42097 Wuppertal, Germany

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López Peña, Javier; Lorscheid, Oliver. Projective geometry for blueprints. Comptes Rendus. Mathématique, Tome 350 (2012) no. 9-10, pp. 455-458. doi : 10.1016/j.crma.2012.05.001. http://archive.numdam.org/articles/10.1016/j.crma.2012.05.001/

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