Commentarii Mathematici Helvetici
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Published online: 2000-12-31
Strong approximation for Zariski dense subgroups over arbitrary global fieldsRichard Pink (1) ETH Zürich, Switzerland
Consider a finitely generated Zariski dense subgroup $ \Gamma $ of a connected simple algebraic group G over a global field F. An important aspect of strong approximation is the question of whether the closure of $ \Gamma $ in the group of points of G with coefficients in a ring of partial adeles is open. We prove an essentially optimal result in this direction, based on the condition that $ \Gamma $ is not discrete in that ambient group. There are no restrictions on the characteristic of F or the type of G, and simultaneous approximation in finitely many algebraic groups is also studied. Classification of finite simple groups is not used.
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Pink Richard: Strong approximation for Zariski dense subgroups over arbitrary global fields. Comment. Math. Helv. 75 (2000), 608-643. doi: 10.1007/s000140050142