Tensor functor from Smooth Motives to motives over a base

2011/11/16 by Banerjee, Anandam
#18E30 #19E15 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1111.3718

Abstract

Recently, Levine constructed a DG category whose homotopy category is equivalent to the full subcategory of motives over a base-scheme S generated by the motives of smooth projective S-schemes, assuming that S is itself smooth over a perfect field. In his construction, the tensor structure required ℚ-coefficients. The author has previously shown how to provide a tensor structure on the homotopy category mentioned above, when S is semi-local and essentially smooth over a field of characteristic zero, extending Levine's tensor structure with ℚ-coefficients. In this article, it is shown that, under these conditions, the fully faithful functor ρ_S that Levine constructed from his category of smooth motives to the category DM_S of motives over a base (defined by Cisinski-Déglise) is a tensor functor.

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