Non simplicité du groupe de Cremona sur tout corps  [ Non-simplicity of the Cremona group over any field ]
Annales de l'Institut Fourier, Volume 66 (2016) no. 5, p. 2021-2046

Using a theorem of F. Dahmani, V. Guirardel and D. Osin we prove that the Cremona group in 2 dimension is not simple, over any field. More precisely, we show that some elements of this group satisfy a weakened WPD property which is equivalent in our particular context to the M. Bestvina and K. Fujiwara’s one. (An English version of this paper is available on the webpage of the author.)

En utilisant un théorème de F. Dahmani, V. Guirardel et D. Osin, nous prouvons que le groupe de Cremona de dimension 2 n’est pas simple sur tout corps. Plus précisément, nous montrons que certains éléments de ce groupe satisfont une version affaiblie de la propriété WPD qui est équivalente dans notre contexte particulier à celle de M. Bestvina et K. Fujiwara.

Received : 2015-04-24
Revised : 2015-12-02
Accepted : 2016-02-18
Published online : 2016-07-28
DOI : https://doi.org/10.5802/aif.3056
Classification:  14E07,  20F65
Keywords: Cremona group, WPD property, hyperbolic space
@article{AIF_2016__66_5_2021_0,
     author = {Lonjou, Anne},
     title = {Non simplicit\'e du groupe de Cremona sur tout corps},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {5},
     year = {2016},
     pages = {2021-2046},
     doi = {10.5802/aif.3056},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2016__66_5_2021_0}
}
Lonjou, Anne. Non simplicité du groupe de Cremona sur tout corps. Annales de l'Institut Fourier, Volume 66 (2016) no. 5, pp. 2021-2046. doi : 10.5802/aif.3056. http://www.numdam.org/item/AIF_2016__66_5_2021_0/

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