Resumen de Autour d'un Théorème de Stein

Salah Najib

• Let K be a ¯eld of characteristic zero, K an algebraic closure of K and P(X; Y ) a non constant polynomial, with coe±cients in K. For ¸ 2 K, denote the number of distinct irreducible factors f¸;i in a factorization of P ¡ ¸ over K by n(¸). We rewrite without the jacobian derivation aspect of Stein's proof (1989) for showing the following statement :

  if P is non-composite then P ¸ (n(¸) ¡ 1) is at most equal to deg(P) ¡ 1.