Extended skeletons of poly-stable pairs

Abstract

We introduce the notion of poly-stable pairs of formal schemes over the valuation ring of a non-archimedean field. For such pairs we define and investigate the dual intersection complex. We proceed to develop the so called extended skeleton of a poly-stable pair via an approximation process using the classical skeletons constructed by Berkovich. This is essentially a generalization of a construction by Gubler, Rabinoff and Werner from the strictly semi-stable case to the arbitrary poly-stable case and we extend their results.