[Geometrie projective pour les canevas bleus]
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
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
Accepté le :
Publié le :
Javier López Peña 1 ; Oliver Lorscheid 2
@article{CRMATH_2012__350_9-10_455_0, author = {Javier L\'opez Pe\~na and Oliver Lorscheid}, title = {Projective geometry for blueprints}, journal = {Comptes Rendus. Math\'ematique}, pages = {455--458}, publisher = {Elsevier}, volume = {350}, number = {9-10}, year = {2012}, doi = {10.1016/j.crma.2012.05.001}, language = {en}, }
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/
[1] Sheaves and K-theory for
[2] Characteristic 1, entropy and the absolute point, 2009 (preprint) | arXiv
[3] Schemes over
[4]
[5] Toric singularities, Amer. J. Math., Volume 116 (1994) no. 5, pp. 1073-1099
[6] J. López Peña,
[7] Mapping
[8] Torified varieties and their geometries over
[9] The geometry of blueprints. Part I: Algebraic background and scheme theory, Adv. Math., Volume 229 (2012) no. 3, pp. 1804-1846
[10] The geometry of blueprints. Part II: Tits–Weyl models of algebraic groups, 2012 (preprint) | arXiv
[11] G. Mikhalkin, Tropical geometry, unpublished notes, 2010.
[12] Les variétés sur le corps à un élément, Mosc. Math. J., Volume 4 (2004) no. 1, pp. 217-244 (312)
[13] K. Thas, Notes on
- Flag matroids with coefficients, Advances in Mathematics, Volume 436 (2024), p. 46 (Id/No 109396) | DOI:10.1016/j.aim.2023.109396 | Zbl:1529.05036
- The moduli space of matroids, Advances in Mathematics, Volume 390 (2021), p. 118 (Id/No 107883) | DOI:10.1016/j.aim.2021.107883 | Zbl:1479.05045
- Projective spaces over, Journal of Combinatorial Designs, Volume 27 (2019) no. 2, p. 55 | DOI:10.1002/jcd.21639
-
for everyone, Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV), Volume 120 (2018) no. 2, pp. 83-116 | DOI:10.1365/s13291-018-0177-x | Zbl:1430.14005 - Quasicoherent sheaves on projective schemes over
, Journal of Pure and Applied Algebra, Volume 222 (2018) no. 6, pp. 1337-1354 | DOI:10.1016/j.jpaa.2017.07.001 | Zbl:1420.14006 - Blue schemes, semiring schemes, and relative schemes after Toën and Vaquié, Journal of Algebra, Volume 482 (2017), pp. 264-302 | DOI:10.1016/j.jalgebra.2017.03.023 | Zbl:1401.14015
- Deitmar schemes, graphs and zeta functions, Journal of Geometry and Physics, Volume 117 (2017), pp. 234-266 | DOI:10.1016/j.geomphys.2017.01.027 | Zbl:1401.14010
- Cohomology of congruence schemes, arXiv (2013) | DOI:10.48550/arxiv.1307.6014 | arXiv:1307.6014
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