Recollements for derived categories of enriched functors and triangulated categories of motives

We investigate certain categorical aspects of Voevodsky's triangulated categories of motives. For this, various recollements for Grothendieck categories of enriched functors and their derived categories are established. In order to extend these recollements further with respect to Serre's...

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Bibliographic Details
Published in:Journal of algebra 2022-01, Vol.589, p.238-272
Main Authors: Garkusha, Grigory, Jones, Darren
Format: Article
Language:English
Subjects:
Recollements of Abelian and triangulated categories
Triangulated categories of motives
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Summary:We investigate certain categorical aspects of Voevodsky's triangulated categories of motives. For this, various recollements for Grothendieck categories of enriched functors and their derived categories are established. In order to extend these recollements further with respect to Serre's localization, the concept of the (strict) Voevodsky property for Serre localizing subcategories is introduced. This concept is inspired by the celebrated Voevodsky theorem on homotopy invariant presheaves with transfers. As an application, it is shown that Voevodsky's triangulated categories of motives fit into recollements of derived categories of associated Grothendieck categories of Nisnevich sheaves with specific transfers.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2021.09.020