D. O. Orlov, “Triangulated Categories of Singularities and D-Branes in Landau–Ginzburg Models”, Algebraic geometry: Methods, relations, and applications, Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 246, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 240–262; Proc. Steklov Inst. Math., 246 (2004), 227

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2004, Volume 246, Pages 240–262 (Mi tm158)

This article is cited in 259 scientific papers (total in 259 papers)

Triangulated Categories of Singularities and D-Branes in Landau–Ginzburg Models

D. O. Orlov

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (323 kB) Citations (259)

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Abstract: Triangulated categories of singularities are defined and their main properties are investigated. A connection between categories of such type and categories of D-brane of B type in Landau–Ginzburg models is established. This connection is interesting by its applications to mirror symmetry.

Received in February 2004

Bibliographic databases:

Document Type: Article

UDC: 512.7

Language: Russian

Citation: D. O. Orlov, “Triangulated Categories of Singularities and D-Branes in Landau–Ginzburg Models”, Algebraic geometry: Methods, relations, and applications, Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 246, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 240–262; Proc. Steklov Inst. Math., 246 (2004), 227–248

Citation in format AMSBIB

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\paper Triangulated Categories of Singularities and D-Branes in Landau--Ginzburg Models

\inbook Algebraic geometry: Methods, relations, and applications

\bookinfo Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences

\serial Trudy Mat. Inst. Steklova

\yr 2004

\vol 246

\pages 240--262

\publ Nauka, MAIK «Nauka/Inteperiodika»

\publaddr M.

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\zmath{https://zbmath.org/?q=an:1101.81093}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2003math......2304O}

\transl

\jour Proc. Steklov Inst. Math.

\yr 2004

\vol 246

\pages 227--248

Linking options:

https://www.mathnet.ru/eng/tm158

https://www.mathnet.ru/eng/tm/v246/p240

This publication is cited in the following 259 articles:

Bahlekeh A., Salarian Sh., Takahashi R., Toosi Z., “Spanier-Whitehead Categories of Resolving Subcategories and Comparison With Singularity Categories”, Algebr. Represent. Theory, 25:3 (2022), 595–613
Rump W., “Exact Krull-Schmidt Categories With Finitely Many Indecomposables”, Math. Z., 300:1 (2022), 761–789
Rump W., “The Acyclic Closure of An Exact Category and Its Triangulation”, J. Algebra, 565 (2021), 402–440
Kalck M., “A New Equivalence Between Singularity Categories of Commutative Algebras”, Adv. Math., 390 (2021), 107913
Chen X.-W., “Representability and Autoequivalence Groups”, Math. Proc. Camb. Philos. Soc., 171:3 (2021), PII S0305004121000086, 657–668
Li H., Hu J., Zheng Yu., “When the Schur Functor Induces a Triangle-Equivalence Between Gorenstein Defect Categories”, Sci. China-Math., 2021
Benson D., Iyengar S.B., Krause H., Pevtsova J., “Local Duality For the Singularity Category of a Finite Dimensional Gorenstein Algebra”, Nagoya Math. J., 244 (2021), 1–24
Brunner I., Mayer I., Schmidt-Colinet C., “Topological Defects and Susy Rg Flow”, J. High Energy Phys., 2021, no. 3, 98
Bergh P.A., Jorgensen D.A., Moore W.F., “Totally Acyclic Approximations”, Appl. Categ. Struct., 29:4 (2021), 729–745
Hu J., Geng Yu., Wu J., Li H., “Buchweitz'S Equivalences For Gorenstein Flat Modules With Respect to Semidualizing Modules”, J. Algebra. Appl., 20:2 (2021), 2150006
Booth M., “Singularity Categories Via the Derived Quotient”, Adv. Math., 381 (2021), 107631
Klos F., Roggenkamp D., “Complementary Projection Defects and Decomposition”, J. High Energy Phys., 2021, no. 3, 195
Gao N., Koenig S., Psaroudakis Ch., “Ladders of Recollements of Abelian Categories”, J. Algebra, 579 (2021), 256–302
Lu M., Zhu B., “Singularity Categories of Gorenstein Monomial Algebras”, J. Pure Appl. Algebr., 225:8 (2021), 106651
Brunner I., Klos F., Roggenkamp D., “Phase Transitions in Glsms and Defects”, J. High Energy Phys., 2021, no. 5, 006
Bergh P.A., Thompson P., “Matrix Factorizations For Self-Orthogonal Categories of Modules”, J. Algebra. Appl., 20:3 (2021), 2150037
Wang Zh., “Invariance of the Gerstenhaber Algebra Structure on Tate-Hochschild Cohomology”, J. Inst. Math. Jussieu, 20:3 (2021), PII S1474748019000367, 893–928
Wang Zh., “Gerstenhaber Algebra and Deligne'S Conjecture on the Tate-Hochschild Cohomology”, Trans. Am. Math. Soc., 374:7 (2021), 4537–4577
Faenzi D., Pons-Llopis J., “The Cohen-Macaulay Representation Type of Projective Arithmetically Cohen-Macaulay Varieties”, Epijournal Geom. Algebr., 5 (2021), 8
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

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Труды Математического института имени В. А. Стеклова

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