Publications mathématiques de l'IHÉS

, Volume 117, Issue 1, pp 329–349 | Cite as

Geometric Phantom Categories

  • Sergey Gorchinskiy
  • Dmitri Orlov


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, namely, they has trivial K-motives and, hence, all their higher K-groups are trivial too.


Coherent Sheave Triangulate Category Grothendieck Group Smooth Projective Variety Chow Group 
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© IHES and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Algebra and Number Theory SectionSteklov Mathematical Institute RASMoscowRussia
  2. 2.Algebraic Geometry SectionSteklov Mathematical Institute RASMoscowRussia

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