For perfect fields satisfying , 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 over (subfields of) the complex numbers is not simple for .
Pour les corps parfaits qui satisfont , 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 sur les (sous-corps des) nombres complexes n’est pas simple pour .
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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
@article{AIF_2022__72_1_1_0, author = {Schneider, Julia}, title = {Relations in the {Cremona} group over a perfect field}, journal = {Annales de l'Institut Fourier}, pages = {1--42}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {72}, number = {1}, year = {2022}, doi = {10.5802/aif.3463}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3463/} }
TY - JOUR AU - Schneider, Julia TI - Relations in the Cremona group over a perfect field JO - Annales de l'Institut Fourier PY - 2022 SP - 1 EP - 42 VL - 72 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3463/ DO - 10.5802/aif.3463 LA - en ID - AIF_2022__72_1_1_0 ER -
%0 Journal Article %A Schneider, Julia %T Relations in the Cremona group over a perfect field %J Annales de l'Institut Fourier %D 2022 %P 1-42 %V 72 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3463/ %R 10.5802/aif.3463 %G en %F AIF_2022__72_1_1_0
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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