1-motivic sheaves and the Albanese functor

Details 1-motivic sheaves and the Albanese functor 1-motivic sheaves and the Albanese functor

2006-07-28

arxiv.org/abs/math/0607738v2

Journal of Pure and Applied Algebra Vol. 213, No. 5 (2009) 809-839

Mathematics

Algebraic Geometry

54 pages, fully revised exposition with a new "structure theorem" for 1-motivic sheaves, see Theorem 1.3.10, including finitel

Scientific paper

10.1016/j.jpaa.2008.10.002

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 L\pi_0 and LAlb on DM_{eff}(k) deriving \pi_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 N\'eron-Severi groups and higher Albanese sheaves. The latter may be considered as an algebraic avatar of Deligne (co)homology.

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