Work

Schemes of finite expansion and universally closed curves

Year: 2025

Type: article

Abstract: In algebraic geometry there is a well-known categorical equivalence between the category of normal proper integral curves over a field k and the category of finitely generated field extensions of k of transcendence degree 1. In this paper we generalize this equivalence to the category of normal quasi-compact universally closed separated integral k -schemes of dimension 1 and the category of field extensions of k of transcendence degree 1. Our key technique are morphisms of finite expansion which can be considered as relaxation of morphisms of finite type. Since the schemes in the generalized category have many properties similar to normal proper integral curves, we call them normal integral universally closed curves over k .

Source: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

DOI: 10.1007/s13366-025-00810-0

Author: Matthias Johann Steiner

Institution: University of Klagenfurt

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Technische Universität München, Alpen-Adria-Universität Klagenfurt