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Comptes Rendus Mathématique
Volume 350, n° 9-10
pages 455-458 (mai 2012)
Doi : 10.1016/j.crma.2012.05.001
Received : 8 Mars 2012 ;  accepted : 27 April 2012
Projective geometry for blueprints
Geometrie projective pour les canevas bleus
 

Javier López Peña a, 1 , Oliver Lorscheid b
a Department of Mathematics, University College London, 25 Gower Street, London WC1E 6BT, United Kingdom 
b Department of Mathematics, University of Wuppertal, Gaußstr. 20, 42097 Wuppertal, Germany 

Abstract

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  -model. We discuss this in case of the Grassmannian  .

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Résumé

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  -modèle canonique. Nous discutons cela dans le cas de la Grassmannienne  .

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1  J. López Peñaʼs research was supported by MCIM grant MTM2010-20940-C02-01, research group FQM-266 (Junta de Andalucía) and Max-Planck Institute for Mathematics in Bonn.


© 2012  Published by Elsevier Masson SAS de la part de Académie des sciences.
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