Remarks on 1-motivic sheaves

Abstract

We generalize the construction of the category of 1-motives with torsion ${}^t{M}_1$ (introduced by Barbieri-Viale, Rosenschon and Saito) as well as the construction of the category of 1-motivic sheaves ${\mathrm{Shv}}_1$ (defined by Barbieri-Viale and Kahn) to perfect fields $k$ (without inverting the exponential characteristic). For $k$ transcendental over the prime field we extend a result of Barbieri-Viale and Kahn, showing that ${}^{t}M$ and ${\mathrm{Shv}}_1$ have equivalent bounded derived categories.

14 pages. Shortened, corrected version. Results on Laumon 1-motives will appear in another paper

References in corpus (2)

• Transformation de Fourier generalisee
• Sharp de Rham realization

Cited by in corpus (1)

• Deforming motivic theories I: Pure weight perfect Modules on divisorial schemes