Abstract :
We give an elementary proof of what we call Local Bezout Theorem.
Given a system of n polynomials in n indeterminates with coefficients in a henselian local domain, (V,m,k) ,
which residually defines an isolated point in kn of multiplicity r , we prove (under some additional hypothesis on V ) that there are finitely many zeroes of the system
above the residual zero (i.e., with coordinates
in m ), and the sum of their multiplicities is r . Our proof is based on
techniques of computational algebra.