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.
@article{PMIHES_2013__117__329_0,
author = {Gorchinskiy, Sergey and Orlov, Dmitri},
title = {Geometric {Phantom} {Categories}},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {329--349},
publisher = {Springer-Verlag},
volume = {117},
year = {2013},
doi = {10.1007/s10240-013-0050-5},
mrnumber = {3090263},
zbl = {1285.14018},
language = {en},
url = {http://archive.numdam.org/articles/10.1007/s10240-013-0050-5/}
}
TY - JOUR AU - Gorchinskiy, Sergey AU - Orlov, Dmitri TI - Geometric Phantom Categories JO - Publications Mathématiques de l'IHÉS PY - 2013 SP - 329 EP - 349 VL - 117 PB - Springer-Verlag UR - http://archive.numdam.org/articles/10.1007/s10240-013-0050-5/ DO - 10.1007/s10240-013-0050-5 LA - en ID - PMIHES_2013__117__329_0 ER -
%0 Journal Article %A Gorchinskiy, Sergey %A Orlov, Dmitri %T Geometric Phantom Categories %J Publications Mathématiques de l'IHÉS %D 2013 %P 329-349 %V 117 %I Springer-Verlag %U http://archive.numdam.org/articles/10.1007/s10240-013-0050-5/ %R 10.1007/s10240-013-0050-5 %G en %F PMIHES_2013__117__329_0
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://archive.numdam.org/articles/10.1007/s10240-013-0050-5/
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