Géométrie toroïdale et géométrie analytique non archimédienne. Application au type d’homotopie de certains schémas formels

Abstract

V.G. Berkovich’s non-Archimedean analytic geometry provides a natural framework to understand the combinatorial aspects in the theory of toric varieties and toroidal embeddings. This point of view leads to a conceptual and elementary proof of the following results: if X is an algebraic scheme over a perfect field and if D is the exceptional normal crossing divisor of a resolution of the singularities of X, the homotopy type of the incidence complex of D is an invariant of X. This is a generalization of a theorem due to D. Stepanov.