  Consider the functor describing deformations of a representation of the
fundamental group of a variety X. This paper is chiefly concerned with
establishing an analogue in finite characteristic of a result proved by Goldman
and Millson for compact Kahler manifolds. By applying the Weil Conjectures
instead of Hodge theory, we see that if X is a smooth proper variety defined
over a finite field, and we consider deformations of certain continuous l-adic
representations of the algebraic fundamental group, then the hull of the
deformation functor will be defined by quadratic equations. Moreover, if X is
merely smooth, then the hull will be defined by equations of degree at most
four.
