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.
Bounds for the orders of the finite subgroups of G(k)
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abstract
If k is a commutative field and G a reductive (connected) algebraic group over k, we give bounds for the orders of the finite subgroups of G(k); these bounds depends on the type of G and on the Galois groups of the cyclotomic extensions of k.
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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.