SUPER-APPROXIMATION, II: THE p-ADIC AND BOUNDED POWER OF SQUARE-FREE INTEGERS CASES
نویسنده
چکیده
Let Ω be a finite symmetric subset of GLn(Z[1/q0]), Γ := 〈Ω〉, and let πm be the group homomorphism induced by the quotient map Z[1/q0] → Z[1/q0]/mZ[1/q0]. Then the family of Cayley graphs {Cay(πm(Γ), πm(Ω))}m is a family of expanders as m ranges over fixed powers of square-free integers and powers of primes that are coprime to q0 if and only if the connected component of the Zariski-closure of Γ is perfect. Some of the immediate applications, e.g. orbit equivalence rigidity, largeness of certain `-adic Galois representations, are also discussed.
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