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  1. Home
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  3. Regular and Irregular Holonomic D-Modules
  • Cited by 12
Publisher:
Cambridge University Press
Online publication date:
May 2016
Print publication year:
2016
Online ISBN:
9781316675625
DOI:
https://doi.org/10.1017/CBO9781316675625
Subjects:
Mathematics (general), Mathematics, Geometry and Topology, Algebra
Series:
London Mathematical Society Lecture Note Series (433)
Information

Book description

D-module theory is essentially the algebraic study of systems of linear partial differential equations. This book, the first devoted specifically to holonomic D-modules, provides a unified treatment of both regular and irregular D-modules. The authors begin by recalling the main results of the theory of indsheaves and subanalytic sheaves, explaining in detail the operations on D-modules and their tempered holomorphic solutions. As an application, they obtain the Riemann–Hilbert correspondence for regular holonomic D-modules. In the second part of the book the authors do the same for the sheaf of enhanced tempered solutions of (not necessarily regular) holonomic D-modules. Originating from a series of lectures given at the Institut des Hautes Études Scientifiques in Paris, this book is addressed to graduate students and researchers familiar with the language of sheaves and D-modules, in the derived sense.

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Contents

Contents
  • Introduction
    pp 1-6
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References
References
[An07] E., Andronikof, Interview with Mikio Sato, Not. Am. Math. Soc. 54 no. 2 (2007), 208–222.
[BE04] S., Bloch and H., Esnault, Homology for irregular connections, J. Théor. Nombres Bordeaux 16 (2004), 357–371.
[Be71] I., Bernstein, Modules over a ring of differential operators, Funct. Anal. Appl. 5 (1971), 89–101.
[Bj 93] J.-E., Björk, Analytic D-modules and applications, Kluwer Academic Publisher, Dordrecht, Boston, and London (1993).
[BM88] E., Bierstone and P.-D., Milman, Semi-analytic sets and subanalytic sets, Inst. Hautes Études Sci. Publ. Math. 67 (1988), 5–42.
[De70] P., Deligne, Équations différentielles à points singuliers réguliers, Lect. Notes Math. 163 Springer, Berlin (1970).
[DK13] A., D'Agnolo and M., Kashiwara, Riemann–Hilbert correspondence for irregular holonomic systems, arXiv:1311.2374v1.
[DS96] A., D'Agnolo and P., Schapira, Leray's quantization of projective duality, Duke Math. J. 84 no. 2 (1996), 453–496.
[Ga81] O., Gabber, The integrability of the characteristic variety, Am. J. Math. 103 (1981), 445–468.
[GQS70] V., Guillemin, D., Quillen and S., Sternberg, The integrability of characteristics, Commun. Pure Appl. Math. 23 (1970), 39–77.
[Gr66] A., Grothendieck, On the de Rham cohomology of algebraic varieties, Inst. Hautes Études Sci. Publ. Math. 29 (1966), 93–101.
[GS12] S., Guillermou and P., Schapira, Microlocal theory of sheaves and Tamarkin's non displaceability theorem, Homological Mirror Symmetry and Tropical Geometry, Lecture Notes of the Unione Mathematica Italiana, Springer (2014), 43–85. arXiv:1106.1576v2 (2012).
[Hi 09] M., Hien, Periods for flat algebraic connections, Invent. Math. 178 (2009), 1–22.
[HTT08] R., Hotta, K., Takeuchi and T., Tanisaki, D-modules, perverse sheaves, and representation theory, Prog. Math. 236, Birkhäuser (2008).
[Ka70] M., Kashiwara, Algebraic study of systems of partial differential equations, Thesis, Tokyo University (1970), Mémoires Soc. Math. France (N.S.) 63 (1995).
[Ka75] M., Kashiwara, On the maximally overdetermined system of linear differential equations I, Publ. Res. Inst. Math. Sci. 10 (1974/75), 563–579.
[Ka78] M., Kashiwara, On the holonomic systems of linear differential equations II, Invent. Math. 49 (1978), 121–135.
[Ka80] M., Kashiwara, Faisceaux constructibles et systèmes holonômes d'équations aux dérivées partielles linéaires à points singuliers réguliers, Séminaire Goulaouic-Schwartz, 1979–1980, Exp. No. 19, École Polytech., Palaiseau (1980).
[Ka84] M., Kashiwara, The Riemann–Hilbert problem for holonomic systems, Publ. Res. Inst. Math. Sci. 20 no. 2 (1984), 319–365.
[Ka03] M., Kashiwara, D-modules and microlocal calculus, Translations of Mathematical Monographs, 217, American Math. Soc. (2003).
[Ke 10] K. S., Kedlaya, Good formal structures for flat meromorphic connections, I: Surfaces, Duke Math. J. 154 no. 2 (2010), 343–418.
[Ke 11] K. S., Kedlaya, Good formal structures for flat meromorphic connections, II: Excellent schemes, J. Am. Math. Soc. 24 (2011), 183–229.
[KK81] M., Kashiwara and T., Kawai, On holonomic systems of microdifferential equations III: Systems with regular singularities, Publ. Res. Inst. Math. Sci. 17 (1981), 813–979.
[KL85] N., Katz and G., Laumon, Transformation de Fourier et majoration de sommes d'exponentielles, Inst. Hautes Études Sci. Publ. Math. 63 (1985), 361–418.
[KS90] M., Kashiwara and P., Schapira, Sheaves on manifolds, Grundlehren der Math. Wiss. 292, Springer-Verlag (1990).
[KS96] M., Kashiwara and P., Schapira, Moderate and formal cohomology associated with constructible sheaves, Mem. Soc. Math. France 64 (1996).
[KS97] M., Kashiwara and P., Schapira, Integral transforms with exponential kernels and Laplace transform, J. Am. Math. Soc. 10 (1997), 939–972.
[KS01] M., Kashiwara and P., Schapira, Ind-sheaves, Astérisque Soc. Math. France 271 (2001), 136 pp.
[KS03] M., Kashiwara and P., Schapira, Microlocal study of ind-sheaves I. Microsupport and regularity, Astérisque Soc. Math. France 284 (2003), 143–164.
[KS06] M., Kashiwara and P., Schapira, Categories and sheaves, Grundlehren der Math. Wiss. 332, Springer-Verlag (1990).
[KS14] M., Kashiwara and P., Schapira, Irregular holonomic kernels and Laplace transform, Sel. Mat. (New Series) 22 no. 1 (2016), 55–109.
[KS15] M., Kashiwara and P., Schapira, Lectures on regular and irregular holonomic D-modules, 2015, http://preprints.ihes.fr/2015/M/M-15-08.pdf.
[Lo59] S., Lojasiewicz, Sur le problème de la division, Stud. Math. 8, (1959), 87–136.
[Ma66] B., Malgrange, Ideals of differentiable functions, Tata Institute of Fundamental Research Studies in Mathematics, No. 3, Oxford University Press, London (1967).
[Me84] Z., Mebkhout, Une équivalence de catégories – Une autre équivalence de catégories, Compos. Math. 51 (1984), 55–62 and 63–98.
[Mo09] T., Mochizuki, Good formal structure for meromorphic flat connections on smooth projective surfaces, Algebraic Analysis and Around, Adv. Stud. Pure Math., 54, Math. Soc. Japan, Tokyo (2009), 223–253.
[Mo11] T., Mochizuki, Wild harmonic bundles and wild pure twistor D-modules, Astérisque – Société Mathématique de France 340 (2011), x+607.
[Mr10] G., Morando, Preconstructibility of tempered solutions of holonomic D-modules, Internat. Math. Res. Notices no. 4 (2014), 1125–1151, arXiv:1007.4158, doi:10.1093/imrn/rns247.
[Po74] J. B., Poly, Sur l'homologie des courants à support dans un ensemble semi-analytique, Journnées de géométrie analytique (Univ. Poitiers, 1972), pp. 35–43. Bull. Soc. Math. Suppl. Mem., 38, Soc. Math. France, Paris (1974).
[Pr 08] L., Prelli, Sheaves on subanalytic sites, Rend. Semin. Mat. Univ. Padova 120 (2008), 167–216.
[Ra78] J.-P., Ramis, Additif II à “variations sur le thème GAGA”, Lect. Notes Math. 694 (1978), 280–289.
[Sa00] C., Sabbah, Équations différentielles à points singuliers irréguliers et phénomène de Stokes en dimension 2, Astérisque Soc. Math. France 263 (2000).
[Sc 86] J.-P., Schneiders, Un théorème de dualité pour les modules différentiels, C. R. Acad. Sci. 303 (1986), 235–238.
[Sc 99] J.-P., Schneiders, Quasi-abelian categories and sheaves, Mem. Soc. Math. France 76 (1999), vi+134.
[Sc 07] P., Schapira, Mikio Sato, a visionary of mathematics, Not. Am. Math. Soc., 54, no. 2 (2007), 243–245.
[SGA4] Sém. Géom. Alg. (1963–64) by M., Artin, A., Grothendieck and J.-L., Verdier, Théorie des topos et cohomologie étale des schémas, Lect. Notes Math. Springer, 269, 270, 305 (1972/73), xix+525pp, iv+418, vi+640.
[SKK73] M., Sato, T., Kawai and M., Kashiwara, Microfunctions and pseudodifferential equations, in Komatsu (ed.), Hyperfunctions and pseudodifferential equations, Proceedings Katata 1971, Lect. Notes Math., Springer-Verlag 287 (1973), 265–529.
[Ta 08] D., Tamarkin, Microlocal condition for non-displaceability, arXiv:0809.1584v1.
[VD98] L., Van den Dries, Tame topology and O-Minimal structures, London Math. Soc. Lect. Notes Series, 248 (1998), x+180.

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