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

Urs Hartl, Simon Huesken,
published 2014-02-12

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.

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