Remarks on 1-motivic sheaves

Details Remarks on 1-motivic sheaves Remarks on 1-motivic sheaves

2008-01-21

arxiv.org/abs/0801.3153v2

Mathematics

Algebraic Geometry

20 pages. Partially rewritten. Hypothesis added

Scientific paper

We generalize to perfect fields (without inverting the exponential characteristic) the construction of the category of 1-motives with torsion ${}^tM_1$ (introduced by L. Barbieri-Viale, A. Rosenschon and M. Saito in 2003) as well as the construction of the category of 1-motivic sheaves ${\rm Shv}_1$ defined in a recent paper by L. Barbieri-Viale and B. Kahn. We extend a result of the latter paper showing that ${}^tM$ and ${\rm Shv}_1$ have equivalent bounded derived categories. Over a field of characteristic zero, the previous constructions work also for Laumon 1-motives, i.e. allowing additive factors and formal $k$-groups.

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