Isogenies and Congruence Subgroups
Throughout this paper k will denote a number field and V its set of valuations. Let S be any finite set of valuations including ∞, the set of archimedean valuations of k. For each v∈V, kV will denote the completion of k with respect to v and 0V the ring of integers in kV. We denote by A (resp. A(S)) the ring of integers (resp. S-integers) in k (so that A = A(∞)). Let G, H be linear reductive algebraic groups defined over k and f:G→H be a k-isogeny.
KeywordsGalois Group Congruence Subgroup Versus Versus Versus Versus Versus Maximal Compact Subgroup Quadratic Extension
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