A criterion for good reduction of Drinfeld modules and Anderson motives in terms of local shtukas. (English) Zbl 1417.11112

Hartl, Urs; Hüsken, Simon

Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 15, Spec. Iss., 25-43 (2016).

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