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A criterion for good reduction of Drinfeld modules and Anderson motives in terms of local shtukas. (English) Zbl 1417.11112
Summary: For an Anderson $$A$$-motive over a discretely valued field whose residue field has $$A$$-characteristic $$\varepsilon$$, we prove a criterion for good reduction in terms of its associated local shtuka at $$\varepsilon$$. This yields a criterion for good reduction of Drinfeld modules. Our criterion is the function-field analog of Grothendieck’s [Séminaire de géométrie algébrique du Bois-Marie 1967–1969. Groupes de monodromie en géométrie algébrique (SGA 7 II) par P. Deligne et N. Katz. Exposés X à XXII. Springer, Cham (1973; Zbl 0258.00005), Proposition IX.5.13] and A. J. de Jong [Invent. Math. 134, No. 2, 301–333 (1998; Zbl 0929.14029), 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

##### MSC:
 11G09 Drinfel’d modules; higher-dimensional motives, etc. 14L05 Formal groups, $$p$$-divisible groups
##### Keywords:
Drinfeld modules; Anderson motives; shtukas
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