Super-approximation, II: the -adic case and the case of bounded powers of square-free integers

  • Alireza Salehi Golsefidy

    University of California at San Diego, La Jolla, USA
Super-approximation, II: the $p$-adic case and the case of bounded powers of square-free integers cover
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Abstract

Let be a finite symmetric subset of GL, and , and let be the group homomorphism induced by the quotient map . Then the family {Cay of Cayley graphs is a family of expanders as ranges over fixed powers of square-free integers and powers of primes that are coprime to if and only if the connected component of the Zariski-closure of is perfect. Some of the immediate applications, e.g. orbit equivalence rigidity and largeness of certain -adic Galois representations, are also discussed.

Cite this article

Alireza Salehi Golsefidy, Super-approximation, II: the -adic case and the case of bounded powers of square-free integers. J. Eur. Math. Soc. 21 (2019), no. 7, pp. 2163–2232

DOI 10.4171/JEMS/883