Publications Mathématiques. Institut de Hautes Études Scientifiques, 2013, том 117, выпуск 1, страницы 329–349 DOI: https://doi.org/10.1007/s10240-013-0050-5(Mi ihes1)
Эта публикация цитируется в 27 научных статьях (всего в 27 статьях)
Аннотация:
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.
Поступила в редакцию: 18.11.2012 Исправленный вариант: 18.01.2013
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Тип публикации:
Статья
Язык публикации: английский
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/ihes1
Эта публикация цитируется в следующих 27 статьяx:
Lev Borisov, Kimoi Kemboi, “Non-existence of phantoms on some non-generic blowups of the projective plane”, Proc. Amer. Math. Soc., 2025
Johannes Krah, “A phantom on a rational surface”, Invent. math., 235:3 (2024), 1009
Tomoki Yoshida, “Full exceptional collections of line bundles on the blow-up of P5 along Segre threefold”, manuscripta math., 2024
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
Alexander Vishik, “Torsion Motives”, International Mathematics Research Notices, 2023:23 (2023), 20252
Dmitrii Pirozhkov, “Admissible subcategories of del Pezzo surfaces”, Adv. Math., 424 (2023), 109046
Jean-Louis Colliot-Thélène, Federico Scavia, “Sur la conjecture de Tate entière pour le produit d'une courbe et d'une surface CH0-triviale sur un corps fini”, Rend. Circ. Mat. Palermo, II. Ser, 72:5 (2023), 2895
Theo Raedschelders, Greg Stevenson, “Proper connective differential graded algebras and their geometric realizations”, European Journal of Mathematics, 8:S2 (2022), 574
Ching-Jui Lai, Sai-Kee Yeung, “Exceptional Collection of Objects on Some Fake Projective Planes”, International Mathematics Research Notices, 2022:22 (2022), 17546
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)
Dmitri Orlov, “Finite-dimensional differential graded algebras and their geometric realizations”, Adv. Math., 366 (2020), 107096–33
Shizhuo Zhang, “Applications of toric systems on surfaces”, Journal of Pure and Applied Algebra, 223:3 (2019), 1139
Д. О. Орлов, “Производные некоммутативные схемы, геометрические реализации и конечномерные алгебры”, УМН, 73:5 (2018), 123–182; D. O. Orlov, “Derived noncommutative schemes, geometric realizations, and finite dimensional algebras”, Russian Math. Surveys, 73:5 (2018), 865–918
Charles Vial, “Exceptional collections, and the Néron–Severi lattice for surfaces”, Advances in Mathematics, 305 (2017), 895
Pieter Belmans, Theo Raedschelders, “Embeddings of algebras in derived categories of surfaces”, Proc. Amer. Math. Soc., 145:7 (2017), 2757
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