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

Hartl U., Hüsken S.

Abstract

For an Anderson A-motive over a discretely valued field whose residue field has A-characteristic ε, we prove a criterion for good reduction in terms of its associated local shtuka at ε. This yields a criterion for good reduction of Drinfeld modules. Our criterion is the function-field analog of Grothendieck's [SGA 7, Proposition IX.5.13] and de Jong's [dJ98, 2.5] 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.