Extended skeletons of poly-stable pairs

TL;DR

This paper generalizes the concept of extended skeletons from strictly semi-stable to arbitrary poly-stable pairs of formal schemes over non-archimedean valuation rings, expanding the framework of Berkovich's skeletons.

Contribution

It introduces the notion of poly-stable pairs, defines their dual intersection complex, and develops an extended skeleton construction generalizing previous work to broader cases.

Findings

Extended the construction of skeletons to poly-stable pairs.

Established properties of the dual intersection complex.

Generalized results from strictly semi-stable to poly-stable cases.

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.