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- Title
Super-approximation, II: the p-adic case and the case of bounded powers of square-free integers.
- Authors
Golsefidy, Alireza Salehi
- Abstract
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 ZT1=q0U ! ZT1=q0U=mZT1=q0U. Then the family {Cay(πm(Γ), πm.(Ω))}m of Cayley graphs 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 and largeness of certain ℓ-adic Galois representations, are also discussed.
- Subjects
APPROXIMATION theory; INTEGERS; SET theory; HOMOMORPHISMS; PRIME numbers
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2019, Vol 21, Issue 7, p2163
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/883