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Algebraic actions of discrete groups: the p-adic method

Serge Cantat IRMAR,CNRS Junyi Xie IRMAR,CNRS

Dynamical Systems mathscidoc:1908.01002

Silver Award Paper in 2020

Acta Mathematica, 220, (2), 239 – 295, 2018
We study groups of automorphisms and birational transformations of quasi-projective varieties. Two methods are combined; the first one is based on p-adic analysis, the second makes use of isoperimetric inequalities and Lang–Weil estimates. For instance, we show that, if SLn(Z) acts faithfully on a complex quasi-projective variety X by birational transformations, then dim(X)⩾n−1 and X is rational if dim(X)=n−1.
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@inproceedings{serge2018algebraic,
  title={Algebraic actions of discrete groups: the p-adic method},
  author={Serge Cantat, and Junyi Xie},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190821182811536546435},
  booktitle={Acta Mathematica},
  volume={220},
  number={2},
  pages={239 – 295},
  year={2018},
}
Serge Cantat, and Junyi Xie. Algebraic actions of discrete groups: the p-adic method. 2018. Vol. 220. In Acta Mathematica. pp.239 – 295. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190821182811536546435.
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