Matrix factorizations and singularity categories for stacks

 Access to full text

 Full (PDF)

1. D. Abramovich, A. Corti, A. Vistoli, Twisted bundles and admissible covers, Comm. Algebra 31 (2003), 3547-3648 Zbl1077.14034MR2007376
2. D. Arinkin, R. Bezrukavnikov, Perverse coherent sheaves, Moscow Math. J. 10 (2010), 3-29 Zbl1205.18010MR2668828
3. H. Bass, Big projective modules are free, Illinois J. Math. 7 (1963), 24-31 Zbl0115.26003MR143789
4. I. Brunner, M. Herbst, W. Lerche, J. Walcher, Matrix Factorizations And Mirror Symmetry: The Cubic Curve, (2006), University of Chicago Press MR2270440
5. I. Brunner, D. Roggenkamp, B-type defects in Landau-Ginzburg models, (2007), University of Chicago Press Zbl1326.81187MR2342020
6. R. Buchweitz, G. Greuel, F. Schreyer, Cohen-Macaulay modules on hypersurface singularities II, Invent. Math. 88 (1987), 165-182 Zbl0617.14034MR877011
7. M. Bökstedt, A. Neeman, Homotopy limits in triangulated categories, Compositio Math. 86 (1993), 209-234 Zbl0802.18008MR1214458
8. X.-W. Chen, Unifying two results of D. Orlov, Abhandlungen Mathem. Seminar Univ. Hamburg 80 (2010), 207-212 Zbl1214.18013MR2734686
9. A. I. Efimov, Homological mirror symmetry for curves of higher genus, Adv. Math. 230 (2012), 493-530 Zbl1242.14039MR2914956
10. D. Eisenbud, Homological algebra on a complete intersection, with an application to group representations, Trans. Amer. Math. Soc. 260 (1980), 35-64 Zbl0444.13006MR570778
11. H. Fan, T. Jarvis, Y. Ruan, The Witten equation and its virtual fundamental cycle 
12. H. Fan, T. Jarvis, Y. Ruan, The Witten equation, mirror symmetry and quantum singularity theory Zbl1310.32032
13. L. Gruson, M. Raynaud, Critères de platitude et de projectivité. Techniques de “platification” d’un module, Invent. Math. 13 (1971), 1-89 Zbl0227.14010MR308104
14. M. Herbst, K. Hori, D. Page, Phases Of $N=2$ Theories In $1+1$ Dimensions With Boundary 
15. L. Illusie, Conditions de finitude relative, SGA6, Théorie des intersections et théorème de Riemann-Roch, SGA6, exp. III 225 (1971), Springer-Verlag, Berlin-New York Zbl0229.14009
16. L. Illusie, Existence de résolutions globales, Théorie des intersections et théorème de Riemann-Roch, SGA6, exp. II 225 (1971), Springer-Verlag, Berlin-New York Zbl0241.14002
17. L. Illusie, Géneralités sur les conditions de finitude dans les catégories dérivées, Théorie des intersections et théorème de Riemann-Roch, SGA6, exp. I 225 (1971), Springer-Verlag, Berlin-New York Zbl0229.14010
18. H. Kajiura, K. Saito, A. Takahashi, Matrix factorization and representations of quivers. II. Type ADE case, Adv. Math. 211 (2007), 327-362 Zbl1167.16011MR2313537
19. A. Kapustin, Y. Li, D-branes in Landau-Ginzburg models and algebraic geometry, J. High Energy Phys. (2003) MR2041170
20. A. Kapustin, Y. Li, Topological correlators in Landau-Ginzburg models with boundaries, Adv. Theor. Math. Phys. 7 (2003), 727-749 Zbl1058.81061MR2039036
21. L. Katzarkov, M. Kontsevich, T. Pantev, Hodge theoretic aspects of mirror symmetry, From Hodge theory to integrability and TQFT -geometry (2008), 87-174, Amer. Math. Soc., Providence, RI Zbl1206.14009MR2483750
22. M. Khovanov, L. Rozansky, Matrix factorizations and Link homology, Fund. Math. 199 (2008), 1-91 Zbl1145.57009MR2391017
23. M. Kontsevich, Hodge structures in non-commutative geometry, Non-commutative geometry in mathematics and physics (2008), 1-21, Amer. Math. Soc., Providence, RI Zbl1155.53060MR2444365
24. A. Kresch, On the geometry of Deligne-Mumford stacks, Algebraic geometry (Seattle 2005). Part 1 (2009), 259-271, Amer. Math. Soc., Providence, RI Zbl1169.14001MR2483938
25. D. Orlov, Triangulated categories of singularities and D-branes in Landau-Ginzburg models, Proc. Steklov Inst. Math. (2004), 227-248 Zbl1101.81093MR2101296
26. D. Orlov, Derived categories of coherent sheaves and triangulated categories of singularities, Algebra, arithmetic, and geometry: in honor of Yu. I. Manin II (2009), 503-531, Birkhäuser, Boston Zbl1200.18007MR2641200
27. D. Orlov, Formal completions and idempotent completions of triangulated categories of singularities, Adv. Math. 226 (2011), 206-217 Zbl1216.18012MR2735755
28. A. Polishchuk, A. Vaintrob, Matrix factorizations and cohomological field theories Zbl06576588
29. A. Polishchuk, A. Vaintrob, Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations, Duke Math. J. 161 (2012), 1863-1926 Zbl1249.14001MR2954619
30. L. Positselski, Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence, 212 (2011) Zbl1275.18002MR2830562
31. A. Quintero Vélez, McKay correspondence for Landau-Ginzburg models, Commun. Number Theory Phys. 3 (2009), 173-208 Zbl1169.14011MR2504756
32. M. Romagny, Group actions on stacks and applications, Michigan Math. J. 53 (2005), 209-236 Zbl1100.14001MR2125542
33. E. Segal, Equivalences between GIT quotients of Landau-Ginzburg B-models, Commun. Math. Phys. 304 (2011), 411-432 Zbl1216.81122MR2795327
34. P. Seidel, Homological mirror symmetry for the genus two curve, preprint J. Algebraic Geom. 20 (2011), 727-769 Zbl1226.14028MR2819674
35. R. W. Thomason, Algebraic $K$-theory of group scheme actions, Algebraic topology and algebraic -theory (Princeton, N.J., 1983) (1987), 539-563, Princeton Univ. Press Zbl0701.19002MR921490
36. J. Walcher, Stability of Landau-Ginzburg branes, J. Math. Phys. 46 (2005) Zbl1110.81152MR2165838
37. Y. Yoshino, Cohen-Macaulay modules over Cohen-Macaulay rings, (1990), Cambridge University Press, Cambridge Zbl0745.13003MR1079937