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Publ. Math. Inst. Hautes Études Sci., 2013, Volume 117, Issue 1, Pages 329–349 (Mi ihes1)  

Geometric phantom categories

S. Gorchinskiy, D. Orlov

Steklov Mathematical Institute RAS, Gubkin str. 8, Moscow 119991, Russia

Abstract: 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00145
12-01-31506
12-01-33024
10-01-93113
11-01-00336
11-01-00568
Ministry of Education and Science of the Russian Federation MK-4881.2011.1
5139.2012.1
11.G34.31.0023
S.G. was partially supported by RFBR grants 11-01-00145, 12-01-31506, 12-01-33024, MK-4881.2011.1, NSh grant 5139.2012.1, by AG Laboratory HSE, RF gov. grant, ag. 11.G34.31.0023. D.O. was partially supported by RFBR grants 10-01-93113, 11-01-00336, 11-01-00568, NSh grant 5139.2012.1, by AG Laboratory HSE, RF gov. grant, ag. 11.G34.31.0023.


DOI: https://doi.org/10.1007/s10240-013-0050-5


Bibliographic databases:

Document Type: Article
Received: 18.11.2012
Revised: 18.01.2013
Language: English

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