Compactifying normal algebraic spaces

TL;DR

This paper discusses the existence of compactifications of algebraic spaces, acknowledging prior work by Raoult from 1971, and aims to clarify the historical context for researchers in algebraic geometry.

Contribution

The note provides an accessible exposition of Raoult's 1971 results on compactifying algebraic spaces, emphasizing the importance of historical awareness in mathematical research.

Findings

Raoult's 1971 results on compactification are equivalent to the paper's claims.

The techniques used are similar to those in Raoult's original work.

The paper clarifies the historical context of these results.

Abstract

The author wrote this note after being asked about the existence of compactifications of algebraic spaces. Subsequent to posting the article to the math arXiv, the author learned from Yutakaa Matsuura that the results of this paper had been proved by Raoult in 1971, using the same techniques. Since Raoult's article may be unknown to those working in the field, the author is keeping this preprint on the arXiv server. However, he makes no claim of originality.