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Tensor Structure on Smooth Motives

Published online by Cambridge University Press:  16 May 2011

Anandam Banerjee
Anandam Banerjee
Affiliation:
Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, [email protected]
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Abstract

Recently, Bondarko constructed a DG category of motives, whose homotopy category is equivalent to Voevodsky's category of effective geometric motives, assuming resolution of singularities. Soon after, Levine extended this idea to construct 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 both constructions, the tensor structure requires ℚ-coefficients. In this article, it is 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. This is done by defining a pseudo-tensor structure on the DG category of motives constructed by Levine, which induces a tensor structure on its homotopy category.

Keywords

MotivescorrespondencesDG categorypseudo-tensor structure
Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 1 , February 2012 , pp. 57 - 101
Copyright
Copyright © ISOPP 2011

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