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Nonhomeomorphic conjugates of connected Shimura varieties

James S. Milne and Junecue Suh
Arxiv ID: 0804.1953Last updated: 1/19/2021
We show that conjugation by an automorphism of the complex numbers (as an abstract field) may change the topological fundamental group of a locally symmetric variety over C. As a consequence, we obtain a large class of algebraic varieties defined over number fields with the property that different embeddings of the number field into C give complex varieties with nonisomorphic fundamental groups.

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