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

摘要

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