Nonhomeomorphic conjugates of connected Shimura varieties

Details Nonhomeomorphic conjugates of connected Shimura varieties Nonhomeomorphic conjugates of connected Shimura varieties

2008-04-13

arxiv.org/abs/0804.1953v1

Mathematics

Algebraic Geometry

Scientific paper

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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