PDF полного текста (581 kB) PDF английской версии (329 kB)

DOI: https://doi.org/10.4213/sm1128

Аннотация: В статье доказывается существование некоторого типа эквивалентностей между триангулированными категориями особенностей для многообразий разных размерностей. Этот класс эквивалентностей обобщает так называемую периодичность Кноррера. В качестве следствия получается эквивалентность между категориями D-бран типа B в моделях Ландау–Гинзбурга разных размерностей.
Библиография: 22 названия.

Поступила в редакцию: 10.08.2005

Англоязычная версия:
Sbornik: Mathematics, 2006, Volume 197, Issue 12, Pages 1827–1840
DOI: https://doi.org/10.1070/SM2006v197n12ABEH003824

Реферативные базы данных:

Образец цитирования: Д. О. Орлов, “Триангулированные категории особенностей и эквивалентности между моделями Ландау–Гинзбурга”, Матем. сб., 197:12 (2006), 117–132; D. O. Orlov, “Triangulated categories of singularities and equivalences between Landau–Ginzburg models”, Sb. Math., 197:12 (2006), 1827–1840

Цитирование в формате AMSBIB

Образцы ссылок на эту страницу:

https://www.mathnet.ru/rus/sm1128

https://doi.org/10.4213/sm1128

https://www.mathnet.ru/rus/sm/v197/i12/p117

Эта публикация цитируется в следующих статьяx:

1. V. Yu. Baranovsky, “BGG correspondence for toric complete intersections”, Mosc. Math. J., 7:4 (2007), 581–599        
2. A. Kuznetsov, “Homological projective duality”, Publ. Math. Inst. Hautes Йtudes Sci., 2007, № 105, 157–220      
3. Kuznetsov A., “Lefschetz decompositions and categorical resolutions of singularities”, Selecta Math. (N.S.), 13:4 (2008), 661–696        
4. P. Seidel, “$A_\infty$-subalgebras and natural transformations”, Homology, Homotopy Appl., 10:2 (2008), 83–114          
5. Chen Xiao-Wu, “Singularity categories, Schur functors and triangular matrix rings”, Algebr. Represent. Theory, 12:2-5 (2009), 181–191          
6. Chen Xiao-Wu, “Unifying two results of Orlov on singularity categories”, Abh. Math. Semin. Univ. Hambg., 80:2 (2010), 207–212        
7. A. Kapustin, L. Rozansky, “Three-dimensional topological field theory and symplectic algebraic geometry II”, Commun. Number Theory Phys., 4:3 (2010), 463–549        
8. A. Căldăraru, J. Distler, S. Hellerman, T. Pantev, E. Sharpe, “Non-birational twisted derived equivalences in abelian GLSMs”, Comm. Math. Phys., 294:3 (2010), 605–645      
9. Orlov D., “Formal completions and idempotent completions of triangulated categories of singularities”, Adv. Math., 226:1 (2011), 206–217          
10. Ballard M.R., “Derived categories of sheaves on singular schemes with an application to reconstruction”, Adv. Math., 227:2 (2011), 895–919          
11. D. Kaledin, “Derived Mackey functors”, Mosc. Math. J., 11:4 (2011), 723–803      
12. Dyckerhoff T., “Compact generators in categories of matrix factorizations”, Duke Math. J., 159:2 (2011), 223–274            
13. Kuznetsov A., “Base change for semiorthogonal decompositions”, Compos. Math., 147:3 (2011), 852–876          
14. Lenzing H., de la Peña J.A., “Extended canonical algebras and Fuchsian singularities”, Math. Z., 268:1-2 (2011), 143–167          
15. Segal E., “Equivalence between GIT quotients of Landau-Ginzburg B-models”, Comm. Math. Phys., 304:2 (2011), 411–432            
16. Shipman I., “A geometric approach to Orlov's theorem”, Compos. Math., 148:5 (2012), 1365–1389          
17. Orlov D., “Matrix factorizations for nonaffine LG-models”, Math. Ann., 353:1 (2012), 95–108          
18. Burke J., Walker M.E., “Matrix factorizations over projective schemes”, Homology Homotopy Appl., 14:2 (2012), 37–61          
19. Isik M.U., “Equivalence of the derived category of a variety with a singularity category”, Math. Res. Not. IMRN, 2013, no. 12, 2787–2808          
20. R. Bocklandt, “Toric systems and mirror symmetry”, Compos. Math., 149:1 (2013), 1839–1855          
21. O. Iyama, M. Wemyss, “Singular derived categories of $\mathbb Q$-factorial terminalizations and maximal modification algebras”, Adv. Math., 261 (2014), 85–121          
22. Chen Xiao-Wu, “Singular equivalences induced by homological epimorphisms”, Proc. Amer. Math. Soc., 142:8 (2014), 2633–2640        
23. R. Takahashi, “Reconstruction from Koszul homology and applications to module and derived categories”, Pacific J. Math., 268:1 (2014), 231–248            
24. G. Stevenson, “Duality for bounded derived categories of complete intersections”, Bull. Lond. Math. Soc., 46:2 (2014), 245–257          
25. Stevenson, Greg, “Subcategories of singularity categories via tensor actions”, Compos. Math., 150:2 (2014), 229–272        
26. Addington N.M., Segal E.P., Sharpe E.R., “D-Brane Probes, Branched Double Covers, and Noncommutative Resolutions”, Adv. Theor. Math. Phys., 18:6 (2014), 1369–1436          
27. Ballard M. Favero D. Katzarkov L., “A Category of Kernels For Equivariant Factorizations and Its Implications For Hodge Theory”, Publ. Math. IHES, 2014, no. 120, 1–111        
28. Hailong Dao, Ryo Takahashi, “Upper bounds for dimensions of singularity categories”, Comptes Rendus Mathematique, 2015    
29. Arinkin D., Gaitsgory D., “Singular Support of Coherent Sheaves and the Geometric Langlands Conjecture”, Sel. Math.-New Ser., 21:1 (2015), 1–199        
30. A.I.. Efimov, Leonid Positselski, “Coherent analogues of matrix factorizations and relative singularity categories”, Algebra Number Theory, 9:5 (2015), 1159        
31. Walker M.E., “Chern characters for twisted matrix factorizations and the vanishing of the higher Herbrand difference”, Sel. Math.-New Ser., 22:3 (2016), 1749–1791          
32. Abouzaid M., Auroux D., Katzarkov L., “Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces”, Publ. Math. IHES, 2016, no. 123, 199–282          
33. Iritani H., Mann E., Mignon T., “Quantum Serre Theorem as a Duality Between Quantum D -Modules: Table 1.”, Int. Math. Res. Notices, 2016, no. 9, 2828–2888          
34. Eisenbud D., Peeva I.: Eisenbud, D Peeva, I, Minimal Free Resolutions over Complete Intersections, Lecture Notes in Mathematics, 2152, Springer Int Publishing Ag, 2016, V+      
35. Katzarkov L., Kontsevich M., Pantev T., “Bogomolov-Tian-Todorov Theorems For Landau Ginzburg Models”, J. Differ. Geom., 105:1 (2017), 55–117        
36. Kiem Y.-H., Kim I.-K., Lee H., Lee K.-S., “All complete intersection varieties are Fano visitors”, Adv. Math., 311 (2017), 649–661          
37. Lu M., “Gorenstein Defect Categories of Triangular Matrix Algebras”, J. Algebra, 480 (2017), 346–367          
38. Hirano Yu., “Derived Knorrer Periodicity and Orlov'S Theorem For Gauged Landau-Ginzburg Models”, Compos. Math., 153:5 (2017), 973–1007            
39. Gross M., Katzarkov L., Ruddat H., “Towards Mirror Symmetry For Varieties of General Type”, Adv. Math., 308 (2017), 208–275            
40. Zhang P., “Categorical Resolutions of a Class of Derived Categories”, Sci. China-Math., 61:2, SI (2018), 391–402          
41. Stevenson G., “Filtrations Via Tensor Actions”, Int. Math. Res. Notices, 2018, no. 8, 2535–2558        
42. Favero D., Kelly T.L., “Fractional Calabi-Yau Categories From Landau-Ginzburg Models”, Algebraic Geom., 5:5 (2018), 596–649          
43. Psaroudakis Ch., “A Representation-Theoretic Approach to Recollements of Abelian Categories”, Surveys in Representation Theory of Algebras, Contemporary Mathematics, 716, eds. Martsinkovsky A., Igusa K., Todorov G., Amer Mathematical Soc, 2018, 67–154          
44. А. Г. Кузнецов, “Вложение производных категорий поверхностей Энриквеса в производные категории многообразий Фано”, Изв. РАН. Сер. матем., 83:3 (2019), 127–132          ; A. G. Kuznetsov, “Embedding derived categories of Enriques surfaces in derived categories of Fano varieties”, Izv. Math., 83:3 (2019), 534–539    
45. Hochenegger A., Kalck M., Ploog D., “Spherical Subcategories in Representation Theory”, Math. Z., 291:1-2 (2019), 113–147          
46. Donovan W., Wemyss M., “Twists and Braids For General 3-Fold Flops”, J. Eur. Math. Soc., 21:6 (2019), 1641–1701          
47. Ma X., Zhao T., Huang Zh., “Gorenstein Algebras and Recollements”, Commun. Algebr., 47:9 (2019), 3527–3538        
48. Lu M., “Gorenstein Properties of Simple Gluing Algebras”, Algebr. Represent. Theory, 22:3 (2019), 517–543        
49. Kapustka M., Rampazzo M., “Torelli Problem For Calabi-Yau Threefolds With Glsm Description”, Commun. Number Theory Phys., 13:4 (2019), 725–761        
50. Lu L., “Triangle Equivalences and Gorenstein Schemes”, Int. J. Math. Comput. Sci., 15:1 (2020), 301–307      
51. Fang B., Liu Ch.-Ch.M., Zong Zh., “On the Remodeling Conjecture For Toric Calabi-Yau 3-Orbifolds”, J. Am. Math. Soc., 33:1 (2020), 135–222        
52. Brown M.K., Dyckerhoff T., “Topological K-Theory of Equivariant Singularity Categories”, Homol. Homotopy Appl., 22:2 (2020), 1–29      
53. Fatighenti E., Mongardi G., “Fano Varieties of K3-Type and Ihs Manifolds”, Int. Math. Res. Notices, 2021:4 (2021), 3097–3142      
54. Bayer A., Lahoz M., Macri E., Nuer H., Perry A., Stellari P., “Stability Conditions in Families”, Publ. Math. IHES, 133:1 (2021), 157–325      
55. Jiang Q., Leung N.C., Xie Y., “Categorical Plucker Formula and Homological Projective Duality”, J. Eur. Math. Soc., 23:6 (2021), 1859–1898      
56. Martin Kalck, Nebojsa Pavic, Evgeny Shinder, “Obstructions to semiorthogonal decompositions for singular threefolds I: $\mathrm{K}$-theory”, Mosc. Math. J., 21:3 (2021), 567–592    
57. Pippi M., “Motivic and l-Adic Realizations of the Category of Singularities of the Zero Locus of a Global Section of a Vector Bundle”, Sel. Math.-New Ser., 28:2 (2022), 33      
58. Karmazyn J., Kuznetsov A., Shinder E., “Derived Categories of Singular Surfaces”, J. Eur. Math. Soc., 24:2 (2022), 461–526      
59. Laterveer R., “On the Chow Ring of Fano Varieties on the Fatighenti-Mongardi List”, Commun. Algebr., 50:1 (2022), 131–145      
60. М. В. Бондарко, “Построение новых полуортогональных разложений в арифметической геометрии”, Матем. сб., 215:4 (2024), 81–116    

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles