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 Viale
Ultimo
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.
Settore MAT/02 - Algebra
2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/53906
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