%0 Journal Article
%T Modular representations arising from self-dual $\ell$-adic representations of finite groups
%A A. Silverberg
%A Yu. G. Zarhin
%J Mathematics
%D 1998
%I arXiv
%X Suppose $\ell$ is a prime number, ${\mathbf Q}_\ell$ is the field of $\ell$-adic numbers, ${\mathbf F}_\ell$ is the finite field of $\ell$ elements, and $d$ is a positive integer. Suppose $G$ is a finite subgroup of a symplectic group $Sp_{2d}({\mathbf Q}_\ell)$. We prove that $G$ can be embedded in $Sp_{2d}({\mathbf F}_\ell)$ in such a way that the characteristic polynomials are preserved (mod $\ell$), as long as $\ell>3$.
%U http://arxiv.org/abs/math/9809107v1