Super-approximation, I: $\mathfrak {p}$-adic semisimple case
نویسندگان
چکیده
منابع مشابه
SUPER-APPROXIMATION: p-ADIC SEMISIMPLE CASE
Let k be a number field, Ω be a finite symmetric subset of GLn0 (k), and Γ = 〈Ω〉. Let C(Γ) := {p ∈ Vf (k)| Γ is a bounded subgroup of GLn0 (kp)}, and Γp be the closure of Γ in GLn0 (kp). Assuming that the Zariski-closure of Γ is semisimple, we prove that the family of left translation actions {Γ y Γp}p∈C(Γ) has uniform spectral gap. As a corollary we get that the left translation action Γ y G h...
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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 ...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2016
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnw208