One-motives and a conjecture of Deligne

Niranjan Ramachandran

Published 1998-06-22, updated 2003-02-12Version 3

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 $\ell$ of parts of the \'etale cohomology of arbitrary varieties over number fields and finite fields.