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Uspekhi Mat. Nauk, 2005, Volume 60, Issue 6(366), Pages 231–232 (Mi umn1687)  

This article is cited in 30 scientific papers (total in 30 papers)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

Derived categories of coherent sheaves and motives

D. O. Orlov

Steklov Mathematical Institute, Russian Academy of Sciences


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English version:
Russian Mathematical Surveys, 2005, 60:6, 1242–1244

Bibliographic databases:

ArXiv: math/0512620
MSC: Primary 18E30, 14F05; Secondary 14F42
Presented: А. Г. Сергеев
Accepted: 01.12.2005

Citation: D. O. Orlov, “Derived categories of coherent sheaves and motives”, Uspekhi Mat. Nauk, 60:6(366) (2005), 231–232; Russian Math. Surveys, 60:6 (2005), 1242–1244

Citation in format AMSBIB
\by D.~O.~Orlov
\paper Derived categories of coherent sheaves and motives
\jour Uspekhi Mat. Nauk
\yr 2005
\vol 60
\issue 6(366)
\pages 231--232
\jour Russian Math. Surveys
\yr 2005
\vol 60
\issue 6
\pages 1242--1244

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    1. Laterveer R., “On the Chow Groups of Plucker Hypersurfaces in Grassmannians”, Arch. Math.  crossref  mathscinet  isi
    2. A. S. Dugas, R. Martínez-Villa, “Stable equivalences of graded algebras”, J. Algebra, 320:12 (2008), 4215–4241  crossref  mathscinet  zmath  isi
    3. Lu Di Ming, J. H. Palmieri, Wu Quan Shui, J. J. Zhang, “Koszul equivalences in $A_\infty$-algebras”, New York J. Math., 14 (2008), 325–378  mathscinet  zmath
    4. Proc. Steklov Inst. Math., 264 (2009), 62–69  mathnet  crossref  mathscinet  isi  elib  elib
    5. Arend Bayer, Yu. I. Manin, “Stability conditions, wall-crossing and weighted Gromov–Witten invariants”, Mosc. Math. J., 9:1 (2009), 3–32  mathnet  crossref  mathscinet  zmath
    6. V. Bouchard, A. Klemm, M. Mariño, S. Pasquetti, “Topological open strings on orbifolds”, Comm. Math. Phys., 296:3 (2010), 589–623  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. A. Del Padrone, C. Pedrini, “Derived categories of coherent sheaves and motives of K3 surfaces”, Regulators, Contemp. Math., 571, eds. Gil J., DeJeu R., Lewis J., Naranjo J., Raskind W., Xarles X., Amer. Math. Soc., Providence, RI, 2012, 219–232  crossref  mathscinet  zmath  isi
    8. M. Bernardara, M. Bolognesi, “Categorical Representability and Intermediate Jacobians of Fano Threefolds”, Derived categories in algebraic geometry - Tokyo 2011, EMS Ser. Congr. Rep., ed. Kawamata Y., European Math. Soc., 2012, 1–25  mathscinet  zmath  isi
    9. F. Ivorra, J. Sebag, “Géométrie algébrique par morceaux, $K$-équivalence et motifs”, Enseign. Math. (2), 58:3-4 (2012), 375–403  crossref  mathscinet  zmath
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    11. M. Bernardara, M. Bolognesi, “Derived categories and rationality of conic bundles”, Compos. Math., 149:11 (2013), 1789–1817  crossref  mathscinet  zmath  isi
    12. A. Ananyevskiy, A. Auel, S. Garibaldi, K. Zainoulline, “Exceptional collections of line bundles on projective homogeneous varieties”, Adv. Math., 236 (2013), 111–130  crossref  mathscinet  zmath  isi
    13. M. Ballard, D. Favero, L. Katzarkov, “A category of kernels for equivariant factorizations, II: further implications”, J. Math. Pures Appl. (9), 102:4 (2014), 702–757  crossref  mathscinet  zmath  isi
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    15. Honigs K., “Derived Equivalent Surfaces and Abelian Varieties, and Their Zeta Functions”, 143, no. 10, 2015, 4161–4166  crossref  mathscinet  zmath  isi
    16. Halpern-Leistner D., “the Derived Category of a Git Quotient”, 28, no. 3, 2015, 871–912  mathscinet  zmath  isi
    17. Abuaf R., “Homological Units”, Int. Math. Res. Notices, 2017, no. 22, 6943–6960  crossref  mathscinet  isi
    18. Gorchinskiy S., “Integral Chow Motives of Threefolds With K-Motives of Unit Type”, Bull. Korean. Math. Soc., 54:5 (2017), 1827–1849  crossref  mathscinet  isi
    19. Vial Ch., “Exceptional Collections, and the Neron-Severi Lattice For Surfaces”, Adv. Math., 305 (2017), 895–934  crossref  mathscinet  zmath  isi
    20. Honigs K., “Derived Equivalence, Albanese Varieties, and the Zeta Functions of 3-Dimensional Varieties”, Proc. Amer. Math. Soc., 146:3 (2018), 1005–1013  crossref  mathscinet  zmath  isi
    21. Huybrechts D., “Motives of Derived Equivalent K3 Surfaces”, Abh. Math. Semin. Univ. Hamburg, 88:1 (2018), 201–207  crossref  mathscinet  zmath  isi
    22. Kuznetsov A., Shinder E., “Grothendieck Ring of Varieties, D- and l-Equivalence, and Families of Quadrics”, Sel. Math.-New Ser., 24:4 (2018), 3475–3500  crossref  mathscinet  zmath  isi  scopus
    23. Laterveer R., “On the Motive of Intersections of Two Grassmannians in P-9”, Res. Math. Sci., 5 (2018), 29  crossref  mathscinet  isi
    24. Manin Yu., “Forgotten Motives: the Varieties of Scientific Experience”, Interdiscip. Stud. Complex Syst., 2018, no. 13, 17–24  isi
    25. Achter J.D., Casalaina-Martin S., Vial Ch., “Derived Equivalent Threefolds, Algebraic Representatives, and the Coniveau Filtration”, Math. Proc. Camb. Philos. Soc., 167:1 (2019), 123–131  crossref  isi
    26. Laterveer R., “On the Motive of Ito-Miura-Okawa-Ueda Calabi-Yau Threefolds”, Tokyo J. Math., 42:2 (2019), 399–404  crossref  mathscinet  isi
    27. Frei S., “Moduli Spaces of Sheaves on K3 Surfaces and Galois Representations”, Sel. Math.-New Ser., 26:1 (2020), UNSP 6  crossref  isi
    28. Hosono Sh., Takagi H., “Derived Categories of Artin-Mumford Double Solids”, Kyoto J. Math., 60:1 (2020), 107–177  crossref  isi
    29. Laterveer R., “On the Motive of Kapustka-Rampazzo'S Calabi-Yau Threefolds”, Hokkaido Math. J., 49:2 (2020), 227–245  crossref  mathscinet  isi
    30. Ito A., Miura M., Okawa Sh., Ueda K., “Derived Equivalence and Grothendieck Ring of Varieties: the Case of K3 Surfaces of Degree 12 and Abelian Varieties”, Sel. Math.-New Ser., 26:3 (2020), UNSP 38  crossref  mathscinet  isi
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