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.
Degenerations of twisted maps to algebraic stacks
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abstract
We give a definition of twisted map to a quotient stack with projective good moduli space, and we show that the resulting functor satisfies the existence part of the valuative criterion for properness.
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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.