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

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2018-06-01 DOI:10.4310/ACTA.2018.V220.N2.A2

Serge Cantat, Junyi Xie

引用次数: 19

Abstract

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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离散群的代数作用:$p$-进方法

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

ACS Applied Energy Materials Materials Science-Materials Chemistry

CiteScore

10.30

自引率

6.20%

发文量

1368

期刊介绍： ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.