@article{SM_2006_197_12_a5,
author = {D. O. Orlov},
title = {Triangulated categories of singularities and equivalences between {Landau{\textendash}Ginzburg} models},
journal = {Sbornik. Mathematics},
pages = {1827--1840},
year = {2006},
volume = {197},
number = {12},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2006_197_12_a5/}
}
D. O. Orlov. Triangulated categories of singularities and equivalences between Landau–Ginzburg models. Sbornik. Mathematics, Tome 197 (2006) no. 12, pp. 1827-1840. http://geodesic.mathdoc.fr/item/SM_2006_197_12_a5/
[1] P. Berthelot, A. Grothendieck, L. Illusie, “Théorie des intersections et théorème de Riemann–Roch”, Séminaire de Géométrie Algébrique du Bois-Marie 1966–1967 (SGA 6), Lecture Notes in Math., 225, Springer-Verlag, Berlin, 1971 | MR | Zbl
[2] R. W. Thomason, T. Trobaugh, “Higher algebraic $K$-theory of schemes and of derived categories”, The Grothendieck Festschrift, vol. III, Progr. Math., 88, Birhäuser, Boston, MA, 1990, 247–435 | MR | Zbl
[3] D. O. Orlov, “Triangulirovannye kategorii osobennostei i D-brany v modelyakh Landau–Ginzburga”, Algebraicheskaya geometriya. Metody, svyazi i prilozheniya, Posv. pamyati chl.-korr. RAN A. N. Tyurina, Tr. MIAN, 246, 2004, 240–262 | MR | Zbl
[4] M. Kontsevich, “Homological algebra of mirror symmetry”, Proceedings of the International Congress of Mathematicians (Zürich, 1994), Birkhäuser, Basel, 1995, 120–139 | MR | Zbl
[5] M. R. Douglas, “D-branes, categories and $\mathcal N=1$ supersymmetry”, J. Math. Phys., 42:7 (2001), 2818–2843 | DOI | MR | Zbl
[6] K. Hori, C. Vafa, Mirror symmetry, arXiv: hep-th/0002222 | MR
[7] K. Hori, A. Iqbal, C. Vafa, D-branes and mirror symmetry, arXiv: hep-th/0005247 | MR
[8] P. Seidel, “Vanishing cycles and mutations”, European Congress of Mathematics, vol. II (Barcelona, 2000), 202, Progr. Math., Basel, 2001, 65–85 ; arXiv: math.SG/0007115 | MR | Zbl
[9] J.-L. Verdier, “Categories dérivées. Quelques résultats”, Séminaire de Géométrie Algébrique du Bois-Marie (SGA 4 1/2), Lecture Notes in Math., 569, Springer-Verlag, Berlin, 1977, 262–311 | Zbl
[10] S. I. Gelfand, Yu. I. Manin, Metody gomologicheskoi algebry. Vvedenie v teoriyu kogomologii i proizvodnykh kategorii, Nauka, M., 1988 | MR | Zbl
[11] M. Kashiwara, P. Schapira, Sheaves on manifolds, Springer-Verlag, Berlin, 1994 ; M. Kasivara, P. Shapira, Puchki na mnogoobraziyakh, Mir, M., 1997 | MR | Zbl
[12] B. Keller, “Derived categories and their uses”, Handbook of algebra, vol. 1, eds. M. Hazewinkel, North-Holland, Amsterdam, 1996, 671–701 | MR | Zbl
[13] A. Neeman, Triangulated categories, Ann. of Math. Stud., 148, Princeton Univ. Press, Princeton, NJ, 2001 | MR | Zbl
[14] P. Gabriel, M. Zisman, Calculus of fractions and homotopy theory, Springer-Verlag, Berlin, 1967 ; P. Gabriel, M. Tsisman, Kategorii chastnykh i teoriya gomotopii, Mir, M., 1971 | MR | Zbl | MR | Zbl
[15] R. W. Thomason, “Equivariant resolution, linearization, and Hilbert's fourteenth problem over arbitrary base schemes”, Adv. Math., 65:1 (1987), 16–34 | DOI | MR | Zbl
[16] B. Totaro, “The resolution property for schemes and stacks”, J. Reine Angew. Math., 577 (2004), 1–22 | MR | Zbl
[17] A. I. Bondal, M. M. Kapranov, “Predstavimye funktory, funktory Serra i perestroiki”, Izv. AN SSSR. Ser. matem., 53:6 (1989), 1183–1205 | MR | Zbl
[18] A. Bondal, D. Orlov, Semiorthogonal decomposition for algebraic varieties, Preprint MPIM 95/15, 1995; arXiv: alg-geom/9506012
[19] D. O. Orlov, “Proektivnye rassloeniya, monoidalnye preobrazovaniya i proizvodnye kategorii kogerentnykh puchkov”, Izv. RAN. Ser. matem., 56:4 (1992), 852–862 | MR | Zbl
[20] R. Hartshorne, Residues and duality, Lecture Notes in Math., 20, Springer-Verlag, Berlin, 1966 | MR | Zbl
[21] A. Kuznetsov, “Homological projective duality”, Publ. Math. Inst. Hautes Études Sci., 105 (2007), 157–220 | DOI | MR | Zbl
[22] A. Kapustin, Yi Li, “D-branes in Landau–Ginzburg models and algebraic geometry”, JHEP, 12 (2003), 005 ; arXiv: hep-th/0210296 | DOI | MR