Journal of Algebraic Geometry

Author(s): Niranjan Ramachandran
Journal: J. Algebraic Geom. 13 (2004), 29-80.
Posted: September 22, 2003
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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. Other applications include some cases of conjectures of Serre, Katz, and Jannsen on the independence of $\ell$ of parts of the étale cohomology of arbitrary varieties over number fields and finite fields.

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