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
2023

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.
2023
Settore MAT/03 - Geometria
14A20; 14H25; 14J20; 14D10
   Derived and underived algebraic stacks and applications
   MUR
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/133082
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