Abstract
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 N ℝ such that there exists a fan in N ℝ 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.
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