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Remarks on 1–motivic sheaves

Published online by Cambridge University Press:  13 December 2013

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Abstract

We generalize the construction of the category of 1–motives with torsion in [2] as well as the construction of the category of 1–motivic sheaves Shv1 in [1] to perfect fields k (without inverting the exponential characteristic). For k transcendental over the prime field we extend a result in [1] showing that and Shv1 have equivalent bounded derived categories.

Type
Research Article
Copyright
Copyright © ISOPP 2013 

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References

1.Barbieri-Viale, L., Kahn, B.: On the derived category of 1–motives. arXiv:1009.1900v1 [math.AG].Google Scholar
2.Barbieri-Viale, L., Rosenschon, A., Saito, M.: Deligne's Conjecture on 1-motives, Annals of Math. 158(2) (2003), 593633.Google Scholar
3.Deligne, P.: Théorie de Hodge III, Publ. Math. IHES 44 (1974), 577.Google Scholar
4.Grothendieck, A.: Le groupe de Brauer. III. Exemples et compléments. Dix Exposés sur la Cohomologie des Schémas, pp. 88188, North-Holland, Amsterdam; Masson, Paris, 1968.Google Scholar
5.Grothendieck, A.: A. Grothendieck and others, Groupes de Monodromie en Géométrie Algébrique, SGA 7 I, Lecture Notes in Math. 288, Springer-Verlag, Berlin-New York, 1972.Google Scholar
6.Kashiwara, M., Schapira, P.: Categories and sheaves, Grundlehren der Mathematischen Wissenschaften 332, Springer-Verlag, Berlin, 2006.Google Scholar
7.Milne, J.S.: Étale Cohomology, Princeton Math. Series, Princeton University Press, 1980.Google Scholar
8.Voevodsky, V.: Triangulated categories of motives over a field, in “Cycles, transfers, and motivic homology Theory”, Annals of Math. Studies 143, Princeton University Press, 2000.Google Scholar