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1-motivic sheaves and the Albanese functor

J. Ayoub·L. Barbieri-Viale
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Abstract

We introduce n-generated sheaves and n-motivic sheaves, describing completely for n = 0, 1 and proposing a conjecture for n > 1. We then obtain functors Lπ_0 and LAlb on DM_{eff}(k) deriving π_0 and Alb. The functor LAlb extends the one constructed (by the second author jointly with B.Kahn) to non-necessarily geometric motives. These functors are then used to define higher Néron-Severi groups and higher Albanese sheaves. The latter may be considered as an algebraic avatar of Deligne (co)homology.

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BibTeXRIS

J. Ayoub, L. Barbieri-Viale. 2008-10-21. 1-motivic sheaves and the Albanese functor. https://doi.org/10.1016/j.jpaa.2008.10.002

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