Algebraic spaces that become schematic after ground field extension

TL;DR

This paper constructs examples of algebraic spaces that are not schemes over a base field but become schemes after a finite extension of the ground field, illustrating a nuanced behavior in algebraic geometry.

Contribution

It provides explicit examples of non-schematic algebraic spaces that turn into schemes after finite ground field extensions, highlighting a new phenomenon.

Findings

Examples of non-schematic algebraic spaces becoming schemes after extension

Illustration of how ground field extensions affect algebraic space properties

Insight into the relationship between algebraic spaces and schemes

Abstract

We construct examples of non-schematic algebraic spaces that become schemes after finite ground field extensions.