Valuations centered at a two-dimensional regular local ring: Infima and Topologies

TL;DR

This paper proves that any non-empty set of valuations centered at a two-dimensional regular local ring has an infimum and extends results related to non-metric trees.

Contribution

It introduces a generalization of valuation infima and topological structures in the context of two-dimensional regular local rings.

Findings

Existence of infima for valuation sets in two-dimensional regular local rings

Generalization of non-metric tree results

New topological insights into valuation spaces

Abstract

The aim of this paper is to prove that every non-empty set of valuations centered at a two-dimensional regular domain has an infimum. We also generalize some results related to a non-metric tree.