Vanishing Cycles of Irregular D-Modules

Compositio Mathematica

Volumn 116, Issue 3, 1999, Pages 241-310

  Laurent, Yves ^a  

^a UNIV GRENOBLE ALPES   (France)

Author keywords

D modules; Irregularity; Vanishing cycles

Indexed keywords

EID: 0042639228     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1000791329695     Document Type: Article

References (31)

1. Aoki, T.: Invertibility for microdifferential operators of infinite order, Publ. RIMS Kyoto Univ. 18 (1982), 1-29.
2. Björk, J.-E.: Analytic D-Modules and Applications, Kluwer Acad. Publ., Dordrecht, Boston, London, 1993.
3. Brylinski, J.-L., Dubson, A. and Kashiwara, M.: Formule de l'indice pour les modules holonomes et obstruction d'Euler locale, CR Acad. Sci. Paris série I 293 (1981), 573-577.
4. Brylinski, J.-L., Malgrange, B. and Verdier, J.-L.: Transformation de Fourier géométrique II, CR Acad. Sci. Paris série I 303 (1986), 193-198.
5. Bouter de Monvel, L.: Opérateurs pseudo-différentiels d'ordre infini, Ann. Inst. Fourier Grenoble 22 (1972), 229-268.
6. Ginsburg, V.: Characteristic varieties and vanishing cycles, Invent. Math. 84 (1986), 327-402.
7. Grothendieck, A. and Deligne, P.: SGA 7, Vol. 288, Springer, New York, 1973.
8. Hartshorne, R.: Residues and Duality, Lecture Notes in Math. 20, Springer, New York, 1966.
9. Honda, N.: On the reconstruction theorem of holonomic modules in the Gevrey classes, Publ. RIMS Kyoto Univ. 27 (1991), 923-943.
10. Honda, N.: Regularity theorems for holonomic modules, Proc. Japan Acad. Ser. A 69 (1993), 111-114.
11. Kashiwara, M.: Systems of Microdifferential Equations, Progr. Math. 34, Birkhäuser, Basel, 1983.
12. Kashiwara, M.: Vanishing Cycles and Holonomic Systems of Differential Equations, Lecture Notes in Math. 1016, Springer, New York, 1983, pp. 134-142.
13. Kashiwara, M.: Index theorem for constructible sheaves, Astérisque 130 (1985), 193-209.
14. Kashiwara, M. and Kawaï, T.: Second microlocalization and asymptotic expansions, In: Complex Analysis, Microlocal Calculus and Relativistic Quantum Theory, Lecture Notes in Phys. 126, Springer, New York, 1980, pp. 21-76.
15. Kashiwara, M. and Kawaï, T.: On the holonomic systems of microdifferential equations III. Systems with regular singularities, Publ. RIMS, Kyoto Univ. 17 (1981), 813-979.
16. Kashiwara, M. and Schapira, P.: Microlocal study of sheaves, Astérisque 128 (1985).
17. Kashiwara, M. and Schapira, P.: Sheaves on Manifolds, Grundlehren der Math. 292, Springer, Berlin, 1990.
18. Laurent, Y.: Théorie de la deuxième microlocalisation dans le domaine complexe, Progr. Math. 53, Birkhäuser, Basel, 1985.
19. Laurent, Y.: Polygone de Newton et b-fonctions pour les modules microdifférentiels, Ann. Ecole Norm. Sup. Ser. 4 20 (1987), 391-441.
20. Laurent, Y.: Microlocal operators with plurisubharmonic growth, Compositio Math. 86 (1993), 23-67.
21. Laurent, Y.: Vanishing cycles of D-modules, Invent. Math. 112 (1983), 491-539.
22. Laurent, Y. and Malgrange, B.: Cycles proches, spécialisation et D-modules, Ann. Inst. Fourier Grenoble 45 (1995).
23. Malgrange, B.: Polynome de Berstein-Sato et cohomologie évanescente, Analyse et topologie sur les espaces singuliers, Astérisque 101-102 (1983).
24. Malgrange, B.: Equations différentielles à coefficients polynomiaux, Progr. Math. 96, Birkhäuser, Boston, 1991.
25. Ramis, J.-P.: Dévissage Gevrey, Astérisque 59-60 (1978), 173-204.
26. Ramis, J.-P.: Théorèmes d'indices Gevrey pour les équations différentielles ordinaires, Mem. Amer. Math. Soc. 48 (1984), 296.
27. Sabbah, C.: D-modules et cycles évanescents, géométrie réelle, Travaux en Cours 24, Hermann, Paris, 1987, pp. 53-98.
28. Sabbah, C. and Mebkhout, Z.: D-Nodules et cycles évanescents, Travaux en Cours 35, Hermann, Paris, 1988.
29. Sato, M., Kawaï, T. and Kashiwara, M.: Hyperfunctions and Pseudo-differential Equations, Lect. Notes in Math. 287, Springer, New York, 1980, pp. 265-529.
30. Sato, M., Kawaï, T. and Kashiwara, M.: Microlocal analysis of theta functions, Adv. Stud. Pure Math. 4 (1984), 267-289.
31. Schapira, P.: Microdifferential Systems in the Complex Domain, Grundlehren der Math. 269, Springer, Berlin, 1985.