S-equivalence for algebraic stacks

Abstract

We generalize the notion of S-equivalence, previously defined for semistable vector bundles, to points in arbitrary algebraic stacks and use it to describe the identification of points when passing to the moduli space. As applications, we recover the classical S-equivalence by considering the identification of semistable vector bundles in the moduli space, and discuss its relation to separatedness of the moduli space.