Pure Anderson Motives and Abelian τ-Sheaves

Details Pure Anderson Motives and Abelian τ-Sheaves Pure Anderson Motives and Abelian τ-Sheaves

2007-09-18

arxiv.org/abs/0709.2809v2

Mathematics

Number Theory

final version as it appears in Mathematische Zeitschrift

Scientific paper

10.1007/s00209-009-0661-1

Pure t-motives were introduced by G. Anderson as higher dimensional generalizations of Drinfeld modules, and as the appropriate analogs of abelian varieties in the arithmetic of function fields. In order to construct moduli spaces for pure t-motives the second author has previously introduced the concept of abelian \tau-sheaf. In this article we clarify the relation between pure t-motives and abelian \tau-sheaves. We obtain an equivalence of the respective quasi-isogeny categories. Furthermore, we develop the elementary theory of both structures regarding morphisms, isogenies, Tate modules, and local shtukas. The later are the analogs of p-divisible groups.

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