no. 1
Relations in the Cremona group over a perfect field
[Relations dans le groupe de Cremona sur un corps parfait]
Schneider, Julia1
1 Universität Basel Departement Mathematik und Informatik Spiegelgasse 1 CH-4051 Basel (Switzerland)
Annales de l'Institut Fourier, Tome 72 (2022) no. 1, pp. 1-42.

Pour les corps parfaits k qui satisfont [k ¯:k]>2, nous construisons de nouveaux sous-groupes distingués du groupe de Cremona du plan et nous donnons une preuve élémentaire de sa non-simplicité en suivant la mélodie de la preuve récente de Blanc, Lamy et Zimmermann du fait que le groupe de Cremona de rang n sur les (sous-corps des) nombres complexes n’est pas simple pour n≥3.

For perfect fields k satisfying [k ¯:k]>2, we construct new normal subgroups of the plane Cremona group and provide an elementary proof of its non-simplicity, following the melody of the recent proof by Blanc, Lamy and Zimmermann that the Cremona group of rank n over (subfields of) the complex numbers is not simple for n≥3.

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Révisé le :
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DOI : 10.5802/aif.3463
Classification : 14E07, 14G27, 14E05, 14J26
Keywords: Cremona groups, normal subgroups, relations, conic bundles, Sarkisov links, Galois action, non-closed fields
Mot clés : groupes de Cremona, sous-groupes normaux, relations, fibrés en coniques, Sarkisov links, action du groupe de Galois, corps non-clos
Schneider, Julia 1

1 Universität Basel Departement Mathematik und Informatik Spiegelgasse 1 CH-4051 Basel (Switzerland)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Schneider, Julia. Relations in the Cremona group over a perfect field. Annales de l'Institut Fourier, Tome 72 (2022) no. 1, pp. 1-42. doi : 10.5802/aif.3463. https://aif.centre-mersenne.org/articles/10.5802/aif.3463/

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