One-motives and a conjecture of Deligne
arXiv:math/9806117 · doi:10.1090/S1056-3911-03-00370-9
Abstract
We introduce new motivic invariants of arbitrary varieties over a perfect field. These cohomological invariants take values in the category of one-motives (considered up to isogeny in positive characteristic). The algebraic definition of these invariants presented here proves a conjecture of Deligne. Applications include some cases of conjectures of Serre, Katz and Jannsen on the independence of of parts of the étale cohomology of arbitrary varieties over number fields and finite fields.
arXiv comment43 pages, latex file, uses amsart, amscd packages (Major revisions; final version). Journal of Algebraic Geometry (to appear)