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One-motives and a conjecture of Deligne

Niranjan Ramachandran
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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. 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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Niranjan Ramachandran. 1998-06-22. One-motives and a conjecture of Deligne. https://doi.org/10.1090/s1056-3911-03-00370-9

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