Mathematical Research Letters

Volume 7 (2000)

Number 4

Reducibility mod $p$ of integral closed subschemes in projective spaces –- an application of arithmetic Bézout

Pages: 405 – 410



Reinie Erné (Université de Rennes I)


In \cite{Erne:preprint99-11}, we showed that we can improve results by Emmy Noether and Alexander Ostrowski (\cite{Schmidt}) concerning the reducibility modulo $p$ of absolutely irreducible polynomials with integer coefficients by giving the problem a geometric turn and using an arithmetic Bézout theorem (\cite{BGS}). This paper is a generalization of \cite{Erne:preprint99-11}, where we show that combining the methods of \cite{Erne:preprint99-11} with the theory of Chow forms leads to similar results for integral, closed subschemes of arbitrary codimension in $\bf P^{s}_{\Z}$.

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