Let X be a smooth separated geometrically connected variety over finite field F_q and f: Y -> X a smooth projective morphism. Let t be a geometric point of X and w a non-negative integer. A celebrated result of Deligne states that the geometric etale fundamental group Pi of X is semisimple on the l-adic cohomology group H^w(Y_t, Q_l) for all prime l not dividing q. By comparing the invariant dimensions of sufficiently many l-adic and mod l representations arising from H^w(Y_t, Q_l) and H^w(Y_t, F_l) respectively, we prove that Pi is semisimple on the F_l-cohomology group H^w(Y_t, F_l) for all sufficiently large l, generalizing Deligne's result. This is a joint work with Anna Cadoret and Akio Tamagawa.