Commentarii Mathematici Helvetici


Full-Text PDF (540 KB) | Metadata | Table of Contents | CMH summary
Volume 75, Issue 4, 2000, pp. 608–643
DOI: 10.1007/s000140050142

Published online: 2000-12-31

Strong approximation for Zariski dense subgroups over arbitrary global fields

Richard Pink[1]

(1) ETH Z├╝rich, 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.

No keywords available for this article.

Pink Richard: Strong approximation for Zariski dense subgroups over arbitrary global fields. Comment. Math. Helv. 75 (2000), 608-643. doi: 10.1007/s000140050142