Relations in the Cremona group over a perfect field
Annales de l'Institut Fourier, Volume 72 (2022) no. 1, pp. 1-42.

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 n3.

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 n3.

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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
Schneider, Julia 1

1 Universität Basel Departement Mathematik und Informatik Spiegelgasse 1 CH-4051 Basel (Switzerland)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Schneider, Julia. Relations in the Cremona group over a perfect field. Annales de l'Institut Fourier, Volume 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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