ON THE REDUCTION MODULE-P OF AN ABSOLUTELY IRREDUCIBLE POLYNOMIAL F(X, Y)

Let f is an element of [x, y] be an absolutely irreducible polynomial. A classical result by Ostrowski states that the reduction module p of f remains absolutely irreducible for all large prime numbers p. Here we give a new sufficient condition on p for the conclusion to hold. Th e result, which holds for polynomials defined over arbitrary discrete valuation rings, also implies equality of the genera of the curves def ined by f and its reduction. The method of proof stems from Hensel's p rinciple and analytic continuation of p-adic analytic functions, follo wing Dwork and Robba.