1-motivic sheaves and the Albanese functor
Algebraic Geometry
2009-09-07 v2
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.
Keywords
Cite
@article{arxiv.math/0607738,
title = {1-motivic sheaves and the Albanese functor},
author = {J. Ayoub and L. Barbieri-Viale},
journal= {arXiv preprint arXiv:math/0607738},
year = {2009}
}
Comments
54 pages, fully revised exposition with a new "structure theorem" for 1-motivic sheaves, see Theorem 1.3.10, including finitely presented (or constructible) 1-motivic sheaves