Regularization of birational actions of FW groups
Confluentes Mathematici, Tome 12 (2020) no. 2, pp. 3-10.

We prove that every birational action of a group with Property FW can be regularized.

Reçu le :
Accepté le :
Accepté après révision le :
Publié le :
DOI : https://doi.org/10.5802/cml.65
Classification : 14E07,  14J50,  20B07,  20M18
Mots clés : birational action, regularization, Property FW, Kazhdan’s property T, partial action
@article{CML_2020__12_2_3_0,
     author = {Yves Cornulier},
     title = {Regularization of birational actions of {FW} groups},
     journal = {Confluentes Mathematici},
     pages = {3--10},
     publisher = {Institut Camille Jordan},
     volume = {12},
     number = {2},
     year = {2020},
     doi = {10.5802/cml.65},
     language = {en},
     url = {https://cml.centre-mersenne.org/articles/10.5802/cml.65/}
}
Yves Cornulier. Regularization of birational actions of FW groups. Confluentes Mathematici, Tome 12 (2020) no. 2, pp. 3-10. doi : 10.5802/cml.65. https://cml.centre-mersenne.org/articles/10.5802/cml.65/

[1] F. Abadie. Sobre ações parciais, fibrados de Fell e grupóides. PhD Thesis, University of São Paulo, 1999.

[2] F. Abadie. Enveloping actions and Takai duality for partial actions. J. Func. Anal. 197:14–67, 2003. | Article | MR 1957674 | Zbl 1036.46037

[3] O. Benoist. Quasi-projectivity of normal varieties. Int. Math. Res. Not. IMRN 17:3878–3885, 2013. | Article | MR 3096912 | Zbl 1312.14022

[4] H. Bass, A. Lubotzky. Automorphisms of groups and of schemes of finite type. Israel J. Math. 44(1):1–22, 1983. | Article | MR 693651 | Zbl 0517.14015

[5] Y. Cornulier. Commensurating actions for groups of piecewise continuous transformations. ArXiv:1803.08572.

[6] Y. Cornulier. Group actions with commensurated subsets, wallings and cubings. ArXiv:1302.5982.

[7] S. Cantat, Y. Cornulier. Commensurating actions of birational groups and groups of pseudo-automorphisms. J. Éc. polytech. Math. 6:767–809, 2019. | Article | MR 4014636 | Zbl 07114038

[8] S. Cantat, J. Xie. Algebraic actions of discrete groups: The p-adic method. Acta Math. 220(2):239–295, 2018. | Article | MR 3849285 | Zbl 1453.14042

[9] S. Cantat, A. Zeghib. Holomorphic actions, Kummer examples, and Zimmer program. Ann. Sci. Éc. Norm. Sup. (4) 45(3):447–489, 2012. | Article | MR 3014483 | Zbl 1280.22015

[10] R. Exel. Partial actions of groups and actions of inverse semigroups, Proc. Amer. Math. Soc. 126(12):3481–3494, 1998. | Article | MR 1469405 | Zbl 0910.46041

[11] J. Kellendonk and M. Lawson. Partial actions of groups. Int. J. Alg. Comput. 14 (1):87–114, 2004. | Article | MR 2041539 | Zbl 1056.20047

[12] A. Lonjou, C. Urech. Actions of Cremona groups on CAT(0) cube complexes. Duke Math. J., to appear. ArXiv:2001.00783, Jan. 2020.

[13] B. Neumann. Groups covered by finitely many cosets. Publ. Math. Debrecen 3:227–242, 1954. | Zbl 0057.25603