Quasi-affineness and the 1-Resolution Property

TL;DR

This paper establishes that normal algebraic spaces with the 1-resolution property are quasi-affine, and extends this result to algebraic stacks, showing they admit finite flat covers by quasi-affine schemes under certain conditions.

Contribution

It proves that the 1-resolution property implies quasi-affineness for normal algebraic spaces and extends the result to algebraic stacks with similar hypotheses.

Findings

Normal algebraic spaces with the 1-resolution property are quasi-affine.

Algebraic stacks with the 1-resolution property have finite flat covers by quasi-affine schemes.

The results hold under mild hypotheses.

Abstract

We prove that, under mild hypothesis, every normal algebraic space which satisfies the $1$-resolution property is quasi-affine. More generally, we show that for algebraic stacks satisfying similar hypotheses, the 1-resolution property guarantees the existence of a finite flat cover by a quasi-affine scheme.