One-motives and a conjecture of Deligne

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 [1] conjecture of Deligne. Other applications include some cases of conjectures of Serre, Katz, and Jannsen on the independence of ℓ \ell of parts of the étale cohomology of arbitrary varieties over number fields and finite [1] fields.