Reducibility mod p of integral closed subschemes in projective

Abstract

In an earlier paper we showed that we can improve results by Emmy Noether and Alexander Ostrowski concerning the reducibility modulo p of absolutely irreducible polynomials with integer coefficients by giving the problem a geometric turn and using an arithmetic Bezout theorem. This paper is a generalization, where we show that combining the methods of that paper with the theory of Chow forms leads to similar results for flat, equidimensional, integral, closed subschemes of arbitrary codimension in a projective space over the ring of rational integers.