Distinguishing Algebraic Spaces from Schemes

2024/11/11 by Herrero, Andres Fernandez, Weißmann, Dario, Zhang, Xucheng
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.07169

Abstract

We introduce local invariants of algebraic spaces and stacks which measure how far they are from being a scheme. Using these invariants, we develop mostly topological criteria to determine when the moduli space of a stack is a scheme. As an application we study moduli of principal bundles on a smooth projective curve.

Related

• "Scheme-theoretic images" of morphisms of stacks
• Algebraic stacks
• Relative dimension of morphisms and dimension for algebraic stacks
• The moduli stack of G-bundles
• Stratifying quotient stacks and moduli stacks