Desingularization of arithmetic surfaces: algorithmic aspects

TL;DR

This paper explores algorithmic methods for desingularizing arithmetic surfaces, combining valuation and chart-based approaches to improve the process through a concrete example.

Contribution

It introduces a novel combined approach leveraging valuation and chart techniques for desingularization of arithmetic surfaces.

Findings

Combining valuation and chart methods can enhance desingularization.

A concrete example demonstrates the benefits of the combined approach.

The approach offers new insights into algorithmic desingularization processes.

Abstract

The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly beneficial it can be to exploit properties and techniques from both worlds simultaneously.