The valuative criterion for proper maps of schemes has many applications in arithmetic, e.g. specializing Q(p)-points to F-p-points. For algebraic stacks, the usual valuative criterion for proper maps is ill-suited for these kind of arguments, since it only gives a specialization point defined over an extension of the residue field, e.g. a Q(p)-point will specialize to an F-pn-point for some n. We give a new valuative criterion for proper maps of tame stacks which solves this problem and is well-suited for arithmetic applications. As a consequence, we prove that the Lang-Nishimura theorem holds for tame stacks.
An arithmetic valuative criterion for proper maps of tame algebraic stacks
Bresciani, Giulio;Vistoli Angelo
2024
Abstract
The valuative criterion for proper maps of schemes has many applications in arithmetic, e.g. specializing Q(p)-points to F-p-points. For algebraic stacks, the usual valuative criterion for proper maps is ill-suited for these kind of arguments, since it only gives a specialization point defined over an extension of the residue field, e.g. a Q(p)-point will specialize to an F-pn-point for some n. We give a new valuative criterion for proper maps of tame stacks which solves this problem and is well-suited for arithmetic applications. As a consequence, we prove that the Lang-Nishimura theorem holds for tame stacks.File in questo prodotto:
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