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Article

Geometric phantom categories

Publications Mathématiques de l'IHÉS. 2013. Vol. 117. No. 1. P. 329-349.
Gorchinskiy Sergey, Orlov D.

In this paper we give a construction of phantom categories, i.e. admissible triangulated subcategories in bounded derived categories of coherent sheaves on smooth projective varieties that have trivial Hochschild homology and trivial Grothendieck group. We also prove that these phantom categories are phantoms in a stronger sense and all their higher K-groups are trivial too.