Geometric Phantom Categories
Gorchinskiy, Sergey1 ; Orlov, Dmitri2
1 Algebra and Number Theory Section, Steklov Mathematical Institute RAS Gubkin str. 8, Moscow, 119991 Russia
2 Algebraic Geometry Section, Steklov Mathematical Institute RAS Gubkin str. 8, Moscow, 119991 Russia
Publications Mathématiques de l'IHÉS, Tome 117 (2013), pp. 329-349.

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.

DOI : 10.1007/s10240-013-0050-5
Gorchinskiy, Sergey 1 ; Orlov, Dmitri 2

1 Algebra and Number Theory Section, Steklov Mathematical Institute RAS Gubkin str. 8, Moscow, 119991 Russia
2 Algebraic Geometry Section, Steklov Mathematical Institute RAS Gubkin str. 8, Moscow, 119991 Russia 
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Gorchinskiy, Sergey; Orlov, Dmitri. Geometric Phantom Categories. Publications Mathématiques de l'IHÉS, Tome 117 (2013), pp. 329-349. doi : 10.1007/s10240-013-0050-5. http://www.numdam.org/articles/10.1007/s10240-013-0050-5/

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