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Mosc. Math. J., 2004, Volume 4, Number 4, Pages 847–868 (Mi mmj173)  

This article is cited in 19 scientific papers (total in 19 papers)

$t$-structures on the derived categories of holonomic $
mathscr D$
-modules and coherent $\mathscr O$-modules


M. Kashiwara

Kyoto University

Abstract: We give the description of the $t$-structure on the derived category of regular holonomic $\mathscr D$-modules corresponding to the trivial $t$-structure on the derived category of constructible sheaves via Riemann–Hilbert correspondence. We give also the condition for a decreasing sequence of families of supports to give a $t$-structure on the derived category of coherent $\mathscr O$-modules.

Key words and phrases: $\mathscr D$-modules, $t$-structures, Riemann–Hilbert correspondence.

Full text: http://www.ams.org/.../abst4-4-2004.html
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MSC: Primary 32C38; Secondary 18E30
Received: February 8, 2003
Language: English

Citation: M. Kashiwara, “$t$-structures on the derived categories of holonomic $
mathscr D$
-modules and coherent $\mathscr O$-modules”, Mosc. Math. J., 4:4 (2004), 847–868

Citation in format AMSBIB
\Bibitem{Kas04}
\by M.~Kashiwara
\paper $t$-structures on the derived categories of holonomic $\\mathscr D$-modules and coherent $\mathscr O$-modules
\jour Mosc. Math.~J.
\yr 2004
\vol 4
\issue 4
\pages 847--868
\mathnet{http://mi.mathnet.ru/mmj173}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2124169}
\zmath{https://zbmath.org/?q=an:1073.14023}


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    This publication is cited in the following articles:
    1. Toda Y., “Limit stable objects on Calabi-Yau 3-folds”, Duke Math. J., 149:1 (2009), 157–208  crossref  mathscinet  zmath  isi  scopus
    2. Bayer A., “Polynomial Bridgeland stability conditions and the large volume limit”, Geometry & Topology, 13 (2009)  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Dmitry Arinkin, Roman Bezrukavnikov, “Perverse coherent sheaves”, Mosc. Math. J., 10:1 (2010), 3–29  mathnet  mathscinet
    4. Toda Yu., “Curve Counting Theories via Stable Objects I. DT/PT Correspondence”, J Amer Math Soc, 23:4 (2010), 1119–1157  crossref  mathscinet  zmath  isi  scopus
    5. Alonso Tarrio L., Jeremias Lopez A., Saorin M., “Compactly generated t-structures on the derived category of a Noetherian ring”, J Algebra, 324:3 (2010), 313–346  crossref  mathscinet  zmath  isi  scopus
    6. Toda Yu., “Generating functions of stable pair invariants via wall-crossings in derived categories”, New Developments in Algebraic Geometry, Integrable Systems and Mirror Symmetry (Rims, Kyoto, 2008), Advanced Studies in Pure Mathematics, 59, 2010, 389–434  mathscinet  zmath  isi
    7. Jardim M., Martins R.V., “The ADHM variety and perverse coherent sheaves”, J Geom Phys, 61:11 (2011), 2219–2232  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    8. Li W.-P., Qin Zh., “Polynomial Bridgeland stability conditions for the derived category of sheaves on surfaces”, Comm Anal Geom, 19:1 (2011), 31–52  crossref  mathscinet  zmath  isi
    9. Meinhardt S., “Stability Conditions on Generic Complex Tori”, Int. J. Math., 23:5 (2012), 1250035  crossref  mathscinet  zmath  isi  scopus
    10. Popa M., “Generic Vanishing Filtrations and Perverse Objects in Derived Categories of Coherent Sheaves”, Derived Categories in Algebraic Geometry - Tokyo 2011, Ems Series of Congress Reports, ed. Kawamata Y., European Mathematical Soc, 2012, 251–278  mathscinet  zmath  isi
    11. A. I. Bondal, “Operations on $t$-structures and perverse coherent sheaves”, Izv. Math., 77:4 (2013), 651–674  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. Fernandes T.M., Sabbah C., “On the de Rham Complex of Mixed Twistor D-Modules”, Int. Math. Res. Notices, 2013, no. 21, 4961–4984  crossref  mathscinet  zmath  isi  scopus
    13. Le Stum B., “Constructible -Modules on Curves”, Sel. Math.-New Ser., 20:2 (2014), 627–674  crossref  mathscinet  zmath  isi  scopus
    14. Vitoria J., “Perverse Coherent T-Structures Through Torsion Theories”, Algebr. Represent. Theory, 17:4 (2014), 1181–1206  crossref  mathscinet  zmath  isi  scopus
    15. Koppensteiner C., “Exact Functors on Perverse Coherent Sheaves”, Compos. Math., 151:9 (2015), 1688–1696  crossref  mathscinet  zmath  isi  scopus
    16. Schnell Ch., “Holonomic D-Modules on Abelian Varieties”, Publ. Math. IHES, 2015, no. 121, 1–55  crossref  mathscinet  zmath  isi  scopus
    17. Henni A.A., Jardim M., Martins R.V., “Adhm Construction of Perverse Instanton Sheaves”, Glasg. Math. J., 57:2 (2015), 285–321  crossref  mathscinet  zmath  isi  elib  scopus
    18. Kashiwara M., “Self-Dual T-Structure”, Publ. Res. Inst. Math. Sci., 52:3 (2016), 271–295  crossref  mathscinet  zmath  isi  scopus
    19. Le Stum B., “Constructible Isocrystals”, Algebr. Number Theory, 10:10 (2016), 2121–2152  crossref  mathscinet  zmath  isi  scopus
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