English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we study the problem of reconstructing the poset structure of ascheme using coverings. For a finite, dominant and separable morphism$X'\to{X}$ of normal, connected Noetherian schemes, we show that the posetstructure of $X'$ can be recovered from the poset structure of $X$ and a set ofGalois gluing data over $X$. This data consists of a set of local Galois orbitsthat are glued using relative Galois groups and transfer maps. To find thisgluing data in practice, we introduce symbolic multivariate Newton-Puiseuxalgorithms that calculate adic approximations of the roots of a univariatepolynomial over chains of prime ideals. By matching power series overintersecting chains of prime ideals, we are then able to glue the local Galoisorbits of the approximations to obtain the global poset structure of thescheme. We show how to apply these algorithms to two types of coverings:coverings of semistable models of curves and sch\"{o}n coverings of very affinevarieties. The first gives an algorithm to calculate the Berkovich skeleton ofa curve, and the second an algorithm to calculate boundary complexes.

Recovering a covering of schemes from Galois orbits of power series