A criterion for good reduction of Drinfeld modules and Anderson motives in terms of local shtukas

TL;DR

This paper establishes a new criterion for good reduction of Anderson A-motives and Drinfeld modules using local shtukas, paralleling classical results for abelian varieties in the function field setting.

Contribution

It introduces a novel criterion for good reduction based on local shtukas, extending classical reduction criteria to Anderson motives and Drinfeld modules.

Findings

Provides a criterion for good reduction in terms of local shtukas.

Applies the criterion specifically to Drinfeld modules.

Establishes an analogy with Grothendieck's and de Jong's criteria for abelian varieties.

Abstract

For an Anderson A-motive over a discretely valued field whose residue field has A-characteristic \epsilon, we prove a criterion for good reduction in terms of its associated local shtuka at \epsilon. This yields a criterion for good reduction of Drinfeld modules. Our criterion is the function-field analog of Grothendieck's and de Jong's criterion for good reduction of an abelian variety over a discretely valued field with residue characteristic p in terms of its associated p-divisible group.