  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.
