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##
Local Bezout Theorem

fichier pdf.

with Mari-Emi Alonso.

Journal of Symbolic Computation ** 45**, (2010), 975-985.
** 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 k^{n} 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.