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We study Serre duality in the singularity category of an isolated Gorenstein singularity and find an explicit formula for the duality pairing in terms of generalised fractions and residues.
H. Cartan and S. Eilenberg, Homological algebra , Princeton Univ. Press, Princeton, NJ, 1956
1956
Earlier work this paper cites.
P. Gabriel, Objets injectifs dans les catégories abéliennes , Séminaire P. Dubriel ( 12 e 12^{e} année 1958 / 1959 1958/1959 ), 17-01 to 17-32
1959
Earlier work this paper cites.
J.-P. Serre, Groupes Algébriques et Corps de Classes , Hermann, Paris (1959)
1959
Earlier work this paper cites.
W. Shih, Homology des espaces fibrés , Inst. des Hautes Études Sci. 13
1962
Earlier work this paper cites.
R. Hartshorne, Residues and duality , Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin, 1966
1966
Earlier work this paper cites.
R. Brown, The twisted Eilenberg-Zilber theorem , Celebrazioni Archimedee del secolo XX, Simposio di topologia (1967), 34–37
1967
Earlier work this paper cites.
J. Tate, Residues of differentials on curves , Ann. Sci. de l’E.N.S. (4) 1 (1968), 149–159
1968
Earlier work this paper cites.
V. K., A. M. Gugenheim, On the chain complex of a fibration , Illinois J. Math. 16
1972
Earlier work this paper cites.
D.G. Northcott, Injective envelopes and inverse polynomials , J. London Math. Soc. (2), 8
1974
Earlier work this paper cites.
M. Auslander, Functors and morphisms determined by objects , Representation theory of algebras (Proc. Conf., Temple Univ., Philadelphia, Pa., 1976), Dekker, New York, 1978, pp. 1–244. Lecture Notes in Pure Appl. Math., Vol. 37
1978
Earlier work this paper cites.
P. Griffiths and J. Harris, Principles of algebraic geometry , Pure and Applied Mathematics, Wiley, 1978
1978
Earlier work this paper cites.
D. Eisenbud, Homological algebra on a complete intersection, with an application to group representations , Trans. Amer. Math. Soc. 260
1980
Earlier work this paper cites.
R.Y. Sharp and H. Zakeri, Modules of generalized fractions , Mathematika 29
1982
Earlier work this paper cites.
J. Lipman, Dualizing sheaves, differentials and residues on algebraic varieties , Astérisque (1984), no. 117, ii+138
1984
Earlier work this paper cites.
R.-O. Buchweitz, Maximal Cohen-Macaulay modules and Tate-cohomology over Gorenstein rings , Unpublished (1987), 155pp. Available from: https://tspace.library.utoronto.ca/handle/1807/16682
1987
Earlier work this paper cites.
R.-O. Buchweitz, G.-M. Greuel and F.-O. Schreyer, Cohen-Macaulay modules on hypersurface singularities II , Invent. Math. 88
1987
Earlier work this paper cites.
H. Knörrer, Cohen-Macaulay modules on hypersurface singularities I , Invent. Math. 88
1987
Cited alongside, same era.
A.I. Bondal and M.M. Kapranov, Representable functors, Serre functors, and reconstructions , Isz. Akad. Nauk SSSR Ser. Mat. 53
1989
Cited alongside, same era.
R. Hübl and E. Kunz, Integration of differential forms on schemes , J. Reine u. Angew. Math. (1990), no. 410, 53–83
1990
Cited alongside, same era.
Y. Yoshino, Cohen-Macaulay modules over Cohen-Macaulay rings , London Mathematical Society Lecture Note Series, vol. 146, Cambridge University Press, Cambridge, 1990
1990
Cited alongside, same era.
J. Lipman and P. Sastry, Regular differentials and equidimensional scheme-maps , J. Alg. Geom. 1 (1992), 101–130
1992
Cited alongside, same era.
F.-S. de Salas, Residue: A geometric construction , Canad. Math. Bull. 45
2002
Later among the works it cites.
A. Kapustin and Y. Li, D-branes in Landau-Ginzburg models and algebraic geometry , J. High Energy Phys. (2003), no. 12, 005, 44 pp. (electronic)
2003
Later among the works it cites.
D. Orlov, Triangulated categories of singularities and D-branes in Landau-Ginzburg models , Tr. Mat. Inst. Steklova 246
2004
Later among the works it cites.
M. Herbst and C.-I. Lazaroiu, Localization and traces in open-closed topological Landau-Ginzburg models , J. High Energy Phys. (2005), no. 5, 044, 31 pp. (electronic)
2005
Later among the works it cites.
H. Krause, The stable derived category of a Noetherian scheme , Compos. Math. 141
2005
Later among the works it cites.
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E. Witten, Mirror manifolds and topological field theory , in Essays on Mirror Manifolds , ed. S.-T. Yau (International Press, 1992)
1992
Cited alongside, same era.
W. Bruns and J. Herzog, Cohen-Macaulay rings , Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993
1993
Cited alongside, same era.
E.E. Enochs and O.M.G. Jenda, Gorenstein injective and projective modules , Math. Z. 220
1995
Cited alongside, same era.
M. Kontsevich, Homological algebra of mirror symmetry , in “Proceedings of the International Congress of Mathematicians”, pages 120–139, Birkhäuser, 1995, arXiv:alg-geom/9411018
1995
Cited alongside, same era.
P. Sastry and A. Yekutieli, On residue complexes, dualizing sheaves and local cohomology modules , Israel J. Math. 90
1995
Cited alongside, same era.
J.-L. Verdier, Des catégories dérivées des catégories abéliennes , Astérisque (1996), no. 239, xii+253 pp. (1997), With a preface by L. Illusie, Edited and with a note by G. Maltsiniotis
1997
Cited alongside, same era.
L.W. Christensen, Gorenstein dimensions , Lecture Notes in Mathematics, vol. 1747, Springer-Verlag, Berlin, 2000
2000
Cited alongside, same era.
C. I. Lazaroiu, On the boundary coupling of topological Landau-Ginzburg models , JHEP 0505 (2005), 037, arXiv:hep-th/0312286
2005
Later among the works it cites.
J. Lipman, S. Nayak, and P. Sastry, Pseudofunctorial behavior of Cousin complexes on formal schemes , Contemporary Mathematics 375
2005
Later among the works it cites.
L.L. Avramov and O. Veliche, Stable cohomology over local rings , Adv. Math. 213 (2007), no. 1, 93–139
2007
Later among the works it cites.
G. M. Greuel, C. Lossen, and E. Shustin, Introduction to singularities and deformations , Springer Monographs in Mathematics, Springer, Berlin, 2007
2007
Later among the works it cites.
P. Jørgensen, Existence of Gorenstein projective resolutions and Tate cohomology , J. Eur. Math. Soc. (JEMS) 9
2007
Later among the works it cites.
I. Burban and Y. Drozd, Maximal Cohen-Macaulay modules over surface singularities , Trends in representation theory of algebras and related topics, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2008, pp. 101–166
2008
Later among the works it cites.
B. Keller, Calabi-Yau triangulated categories , in: Trends in Representation Theory of Algebras, edited by A. Skowronski, European Mathematical Society, Zurich, 2008
2008
Later among the works it cites.
E. Kunz, Residues and duality for projective algebraic varieties , University Lecture Series, vol. 47, American Mathematical Society, 2008
2008
Later among the works it cites.
N. Carqueville, Matrix factorisations and open topological string theory , JHEP 0907:005, 2009
2009
Closest in time.
M. Mackaay, M. Stošić, and P. Vaz, 𝔰 𝔩 ( N ) \mathfrak{sl}(N) -link homology ( N ≥ 4 ) (N\geq 4) using foams and the Kapustin-Li formula , Geom. Topol. 13
2009
Closest in time.