A stacky approach to identifying the semistable locus of bundles

Abstract

We show that the semistable locus is the unique maximal open substack of the moduli stack of principal bundles over a curve that admits a schematic moduli space. For rank $2$ vector bundles it coincides with the unique maximal open substack that admits a separated moduli space, but for higher rank there exist other open substacks that admit separated moduli spaces.

Theorem A now includes the case of semistable principal bundles and the characteristic can be arbitrary in Theorem B and C. To appear in Algebraic Geometry (AG)

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