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Let Γ be an S-arithmetic subgroup of a solvable algebraic group G over an algebraic number field F, such that the finite set S contains at least one place that is nonarchimedean. We construct a certain group H=(ResF/QΓ¯)charSΓ, such that if L is any local field and α:Γ→GLn(L) is any homomorphism, then α virtually extends (modulo a bounded error) to a continuous homomorphism defined on some finite-index...
Let G be a connected, solvable linear algebraic group over a number fieldK, letSbe a finite set of places ofKthat contains all the infinite places, and let O(S) be the ring ofS-integers ofK. We define a certain closed subgroup[formula]of G S =∏ v∈S GK v that contains G O(S) , and prove that G O(S) is a superrigid lattice in[formula], by which we mean that finite-dimensional...
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