算术簇上的Kazhdan定理

摘要：

定义一个算术簇为一个有界对称整环与一个算术群的商。一个算术簇是代数的，这个定理指出当一个复数域的自同构应用于一个算术簇的系数时，所得到的簇又是算术的。这篇文章简化了Kazhdan的证明。特别是，它避免求助于分类定理。它最初于1984年3月28日完成，并以手写形式分发。2001年7月23日：修复了大约30个印刷错误。

英文摘要：

Define an arithmetic variety to be the quotient of a bounded symmetric domain by an arithmetic group. An arithmetic variety is algebraic, and the theorem in question states that when one applies an automorphism of the field of complex numbers to the coefficients of an arithmetic variety the resulting variety is again arithmetic. This article simplifies Kazhdan's proof. In particular, it avoids recourse to the classification theorems. It was originally completed on March 28, 1984, and distributed in handwritten form. July 23, 2001: Fixed about 30 misprints.

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