Some remarks on phantom categories and motives. (English) Zbl 1457.14011
Summary: A phantom category is an admissible subcategory with vanishing Grothendieck group of the bounded derived category of coherent sheaves on a smooth projective variety. The goal of this paper is to study the abstract situation when such a category appears and establish some results which provide evidence for the idea that these categories are invisible on the level of Chow motives.
MSC:
| 14C15 | (Equivariant) Chow groups and rings; motives |
| 14F08 | Derived categories of sheaves, dg categories, and related constructions in algebraic geometry |
| 18G80 | Derived categories, triangulated categories |
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