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Modular embeddings and rigidity for Fuchsian groups. (English) Zbl 1325.20044
Summary: We prove a rigidity theorem for semiarithmetic Fuchsian groups: If \(\Gamma_1\), \(\Gamma_2\) are two semiarithmetic lattices in \(\text{PSL}(2,\mathbb R)\) virtually admitting modular embeddings, and \(f\colon\Gamma_1\to\Gamma_2\) is a group isomorphism that respects the notion of congruence subgroups, then \(f\) is induced by an inner automorphism of \(\text{PGL}(2,\mathbb R)\).
Reviewer: Reviewer (Berlin)

MSC:
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
11F06 Structure of modular groups and generalizations; arithmetic groups
22E40 Discrete subgroups of Lie groups
14G35 Modular and Shimura varieties
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MathOverflow
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