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We show that conjugation by an automorphism of the complex numbers (as anabstract field) may change the topological fundamental group of a locallysymmetric variety over C. As a consequence, we obtain a large class ofalgebraic varieties defined over number fields with the property that differentembeddings of the number field into C give complex varieties with nonisomorphicfundamental groups.

Nonhomeomorphic conjugates of connected Shimura varieties