离散群的代数作用:$p$-进方法

IF 4.9 1区数学 Q1 MATHEMATICS

Acta Mathematica Pub Date : 2018-06-01 DOI:10.4310/ACTA.2018.V220.N2.A2

Serge Cantat, Junyi Xie

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引用次数: 19

摘要

我们研究了拟射影变种的自同构群和对偶变换。两种方法相结合；第一种是基于p-adic分析，第二种是利用等周不等式和LangWeil估计。例如，我们证明了如果SL n（Z）通过对偶变换忠实地作用于复拟投影变种X，那么dim（X）≥n−1，并且如果dim（X）=n−1 X是有理的。

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Algebraic actions of discrete groups: the $p$-adic method

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 LangWeil estimates. For instance, we show that if SL n(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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