摘要翻译：
给定Q的代数闭包Qbar上的一个对象，相应的全纯对象的不变量通常没有理由被绝对Galois群Gal（Qbar/Q）所保持，而且通常这不是真的，尽管在实践中有时观察到这是令人惊讶的。通过Belyi定理，对射影线的覆盖仅在0、1和无穷远点上分支的情况，导出了Grothendieck的dessins D'enfants程序，通过绝对Galois群在这些覆盖上的忠实作用来理解绝对Galois群。这个注释是由Catanese关于一个高维模拟的问题引起的：绝对Galois群是否忠实地作用于光滑曲面的变形等价类？（根据定义，这些等价类当然是最强的变形不变量。）我们给出了一个较弱结果的简短证明：绝对伽罗瓦群忠实地作用于光滑曲面（一般型，正则极化）模空间的不可约分量。Bauer，Catanese和Grunewald最近用不同的结构回答了Catanese最初的问题。
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英文标题：
《Absolute Galois acts faithfully on the components of the moduli space of
  surfaces: A Belyi-type theorem in higher dimension》
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作者：
Robert W. Easton and Ravi Vakil
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Number Theory        数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
  Given an object over the algebraic closure Qbar of Q, there is often no reason for invariants of the corresponding holomorphic object to be preserved by the absolute Galois group Gal(Qbar/Q), and in general this is not true, although it is sometimes surprising to observe in practice. The case of covers of the projective line branched only over the points 0, 1, and infinity, through Belyi's theorem, leads to Grothendieck's dessins d'enfants program for understanding the absolute Galois group through its faithful action on such covers. This note is motivated by Catanese's question about a higher-dimensional analogue: does the absolute Galois group act faithfully on the deformation equivalence classes of smooth surfaces? (These equivalence classes are of course by definition the strongest deformation invariants.) We give a short proof of a weaker result: the absolute Galois group acts faithfully on the irreducible components of the moduli space of smooth surfaces (of general type, canonically polarized). Bauer, Catanese, and Grunewald have recently answered Catanese's original question using a different construction.
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PDF链接：
https://arxiv.org/pdf/0704.3231