  Let X be a smooth quasiprojective subscheme of P^n of dimension m >= 0 over
F_q. Then there exist homogeneous polynomials f over F_q for which the
intersection of X and the hypersurface f=0 is smooth. In fact, the set of such
f has a positive density, equal to zeta_X(m+1)^{-1}, where
zeta_X(s)=Z_X(q^{-s}) is the zeta function of X. An analogue for regular
quasiprojective schemes over Z is proved, assuming the abc conjecture and
another conjecture.
