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

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 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.

15 pages

Cited by in corpus (1)

• Tate modules of isocrystals and good reduction of Drinfeld modules