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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.

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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
\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

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    1. Toda Y., “Limit stable objects on Calabi-Yau 3-folds”, Duke Math. J., 149:1 (2009), 157–208  crossref  mathscinet  zmath  isi  scopus
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    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
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    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
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    14. Vitoria J., “Perverse Coherent T-Structures Through Torsion Theories”, Algebr. Represent. Theory, 17:4 (2014), 1181–1206  crossref  mathscinet  zmath  isi  scopus
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    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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