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.
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.
Received: 18.11.2012 Revised: 18.01.2013
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Language: English
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Giordano Cotti, Boris A. Dubrovin, Davide Guzzetti, Lecture Notes in Mathematics, 2356, Helix Structures in Quantum Cohomology of Fano Varieties, 2024, 79
Young-Hoon Kiem, Kyoung-Seog Lee, Springer Proceedings in Mathematics & Statistics, 409, Birational Geometry, Kähler–Einstein Metrics and Degenerations, 2023, 517
Roland Abuaf, “Hodge numbers and Hodge structures for 3-Calabi–Yau categories”, Annales de la Faculté des sciences de Toulouse : Mathématiques, 32:2 (2023), 337
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Dmitrii Pirozhkov, “Admissible subcategories of del Pezzo surfaces”, Adv. Math., 424 (2023), 109046
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Saša Novaković, “No phantoms in the derived category of curves over arbitrary fields, and derived characterizations of Brauer–Severi varieties”, J. Commut. Algebra, 13:2 (2021)
D. Bergh, S. Gorchinskiy, M. Larsen, V. Lunts, “Categorical measures for finite group actions”, J. Algebraic Geom., 30 (2021), 685–757
Burt Totaro, “The integral cohomology of the Hilbert scheme of points on a surface”, Forum of Mathematics, Sigma, 8 (2020)
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