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.
1-motivic sheaves and the Albanese functor / J. Ayoub, L. Barbieri Viale. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 213:5(2009), pp. 809-839. [10.1016/j.jpaa.2008.10.002]
1-motivic sheaves and the Albanese functor
L. Barbieri VialeUltimo
2009
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 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.Pubblicazioni consigliate
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