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Mathematics of the USSR-Izvestiya, 1990, Volume 35, Issue 3, Pages 519–541
DOI: https://doi.org/10.1070/IM1990v035n03ABEH000716
(Mi im1153)
 

This article is cited in 154 scientific papers (total in 154 papers)

Representable functors, Serre functors, and mutations

A. I. Bondal, M. M. Kapranov
References:
Abstract: This paper studies the categorical version of the concept of mutations of an exceptional set, as used in the theory of vector bundles. The basic object of study is a triangulated category with a family of subcategories satisfying the so-called admissibility condition. A natural notion arising here is that of a Serre functor, effecting a certain duality in the triangulated category.
Bibliography: 16 titles.
Received: 21.06.1988
Bibliographic databases:
Document Type: Article
UDC: 513.6
MSC: Primary 14F05, 18E30; Secondary 18F20
Language: English
Original paper language: Russian
Citation: A. I. Bondal, M. M. Kapranov, “Representable functors, Serre functors, and mutations”, Math. USSR-Izv., 35:3 (1990), 519–541
Citation in format AMSBIB
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\by A.~I.~Bondal, M.~M.~Kapranov
\paper Representable functors, Serre functors, and mutations
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 3
\pages 519--541
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Linking options:
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  • This publication is cited in the following 154 articles:
    1. Huimin Chang, Panyue Zhou, “Mutation of n-cotorsion pairs in triangulated categories”, Journal of Algebra, 2025  crossref
    2. Frédéric Chapoton, “Posets and fractional Calabi–Yau categories”, Mathematics Research Reports, 6 (2025), 1  crossref
    3. M. V. Bondarko, “Producing new semi-orthogonal decompositions in arithmetic geometry”, Sb. Math., 215:4 (2024), 511–542  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. Xiuli Bian, “Classifying Recollements of Derived Module Categories for Derived Discrete Algebras”, Algebr Represent Theor, 27:1 (2024), 279  crossref
    5. Jin Yun Guo, Xiaojian Lu, Yanping Hu, Deren Luo, “ℤ Q type constructions in higher representation theory”, Communications in Algebra, 52:2 (2024), 763  crossref
    6. Henrik Holm, Peter Jørgensen, “The 𝑄-shaped derived category of a ring — compact and perfect objects”, Trans. Amer. Math. Soc., 2024  crossref
    7. David Ayala, Aaron Mazel-Gee, Nick Rozenblyum, “Stratified Noncommutative Geometry”, Memoirs of the AMS, 297:1485 (2024)  crossref
    8. Tobias Dyckerhoff, Mikhail Kapranov, Vadim Schechtman, Yan Soibelman, “Spherical adjunctions of stable -categories and the relative S-construction”, Math. Z., 307:4 (2024)  crossref
    9. Tomoki Yoshida, “Full exceptional collections of line bundles on the blow-up of P5 along Segre threefold”, manuscripta math., 2024  crossref
    10. Russian Math. Surveys, 79:5 (2024), 807–845  mathnet  crossref  crossref  mathscinet  adsnasa
    11. Isambard Goodbody, “Reflecting perfection for finite‐dimensional differential graded algebras”, Bulletin of London Math Soc, 2024  crossref
    12. Jordan Haden, “3-Preprojective Algebras of Type D”, Algebr Represent Theor, 2024  crossref
    13. A. I. Bondal, A. A. Roslyi, “Coherent sheaves, Chern classes, and superconnections on compact complex-analytic manifolds”, Izv. Math., 87:3 (2023), 439–468  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    14. A. V. Fonarev, “Dual exceptional collections on Lagrangian Grassmannians”, Sb. Math., 214:12 (2023), 1779–1800  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    15. Jing He, Panyue Zhou, Xingjia Zhou, “Pre-(n + 2)-angulated categories”, Journal of Algebra, 620 (2023), 452  crossref
    16. Dmitrii Pirozhkov, “Admissible subcategories of del Pezzo surfaces”, Adv. Math., 424 (2023), 109046  mathnet  crossref  isi
    17. Ana Cristina López Martín, Fernando Sancho de Salas, “Indecomposability of derived categories for arbitrary schemes”, Collect. Math., 2023  crossref
    18. Peng Guo, “Exceptional cycles in triangular matrix algebras”, Journal of Algebra, 635 (2023), 235  crossref
    19. Jongmyeong Kim, “Categorical entropy, (co-)t-structures and ST-triples”, Math. Z., 304:3 (2023)  crossref
    20. Wen Chang, Sibylle Schroll, “Exceptional sequences in the derived category of a gentle algebra”, Sel. Math. New Ser., 29:3 (2023)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:3476
    Russian version PDF:1329
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    References:212
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