Comptes Rendus
Algebra/Algebraic Geometry
Projective geometry for blueprints
[Geometrie projective pour les canevas bleus]
Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 455-458.

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 F1-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 F1-model. We discuss this in case of the Grassmannian Gr(2,4).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.05.001

Javier López Peña 1 ; Oliver Lorscheid 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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Javier López Peña; Oliver Lorscheid. Projective geometry for blueprints. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 455-458. doi : 10.1016/j.crma.2012.05.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.05.001/

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