The authors prove a root stack valuative criterion for good moduli spaces and reductive gerbes, enabling root-extension of generic points and several arithmetic and moduli applications.
Loop torsors. Theory and applications
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abstract
Loop torsors over Laurent polynomial rings in characteristic 0 were originally introduced in relation to infinite dimensional Lie theory. Applications to other areas require a theory that can yields results in positive characteristic, and for group schemes that are not of finite type. The relation between loop and so-called toral torsors, is one of the central questions in the area. The present paper addresses this question in full generality.
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Root stack valuative criterion for good moduli spaces
The authors prove a root stack valuative criterion for good moduli spaces and reductive gerbes, enabling root-extension of generic points and several arithmetic and moduli applications.