Continuité des racines d'après Rabinoff.

The content of this paper is a generalization of a theorem by Joseph Rabinoff: if P is a finite family of pointed and rational polyhedra in Nℝ such that there exists a fan in Nℝ that contains all the recession cones of the polyhedra of P, if k is a complete non-archimedean field, if S is a connected and regular k-analytic space (in the sense of Berkovich) and Y is a closed k-analytic subset of U P × k S which is relative complete intersection and contained in the relative interior of U P × k S over S, then the quasifiniteness of π : Y → S implies its flatness and finiteness; moreover, all the finite fibers of π have the same length. This namely gives a analytic justification to the concept of stable intersection used in the theory of tropical intersection. [ABSTRACT FROM AUTHOR]