Rational points Varieties over finite fields 10 Finite fields 4 First Bertini theorem 4 Geometric solutions 4 Normal complete intersection 4 Probabilistic algorithms 4 Second Bertini theorem 4 Straight-line programs 4 Bertini 2 Bertini smoothness theorem 2 Deep holes 2 Deligne estimate 2 Hooley-Katz estimate 2 Multihomogeneous Bézout theorem 2 Polar varieties 2 Reed-solomon codes 2 Singular hypersurfaces 2 Singular locus 2 Symmetric polynomials 2