One-motives and a conjecture of Deligne

Details One-motives and a conjecture of Deligne One-motives and a conjecture of Deligne

1998-06-22

arxiv.org/abs/math/9806117v3

Mathematics

Algebraic Geometry

43 pages, latex file, uses amsart, amscd packages (Major revisions; final version). Journal of Algebraic Geometry (to appear)

Scientific paper

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.

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