We generalize the construction of the category of 1–motives with torsion tM_1, by Barbieri-Viale, Rosenschon and Saito, as well as the construction of the category of 1–motivic sheaves Shv_1, 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 in showing that tM_1 and Shv_1 have equivalent bounded derived categories.
Remarks on 1–motivic sheaves.
BERTAPELLE, ALESSANDRA
2013
Abstract
We generalize the construction of the category of 1–motives with torsion tM_1, by Barbieri-Viale, Rosenschon and Saito, as well as the construction of the category of 1–motivic sheaves Shv_1, 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 in showing that tM_1 and Shv_1 have equivalent bounded derived categories.
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