caa a22 4500 445835745 CHVBK 20180317145329.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00209-009-0661-1 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0661-1 Pure Anderson motives and abelian τ -sheaves [Elektronische Daten] [Matthias Bornhofen, Urs Hartl] 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 τ-sheaf. In this article we clarify the relation between pure t-motives and abelian τ-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. Springer-Verlag, 2010 Bornhofen Matthias Institute of Mathematics, University of Muenster, Einsteinstr. 62, 48149, Muenster, Germany aut Hartl Urs Institute of Mathematics, University of Muenster, Einsteinstr. 62, 48149, Muenster, Germany aut Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 67-100 0025-5874 268:1-2<67 2011 268 209 https://doi.org/10.1007/s00209-009-0661-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0661-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bornhofen Matthias Institute of Mathematics, University of Muenster, Einsteinstr. 62, 48149, Muenster, Germany aut NATIONALLICENCE 700 1- Hartl Urs Institute of Mathematics, University of Muenster, Einsteinstr. 62, 48149, Muenster, Germany aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 67-100 0025-5874 268:1-2<67 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer