Elliptic pairs I. Relative finiteness and duality
Index theorem for elliptic pairs, Astérisque, no. 224 (1994), pp. 5-60.
partie suivante Elliptic pairs II. Euler class and relative index theorem 
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     title = {Elliptic pairs {I.} {Relative} finiteness and duality},
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     year = {1994},
     mrnumber = {1305642},
     zbl = {0856.58038},
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     url = {http://archive.numdam.org/item/AST_1994__224__5_0/}
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Schapira, Pierre; Schneiders, Jean-Pierre. Elliptic pairs I. Relative finiteness and duality, dans Index theorem for elliptic pairs, Astérisque, no. 224 (1994), pp. 5-60. http://archive.numdam.org/item/AST_1994__224__5_0/

[1] M. Atiyah and I. M. Singer, The index of elliptic operators on compact manifolds, Bull. Amer. Math. Soc. 69 (1963), 422-433. | DOI | MR | Zbl

[2] J. M. Bony and P. Schapira, Existence et prolongement des solutions holomorphes des equations aux dérivées partielles, Invent. Math. 17 (1972), 95-105. | DOI | EuDML | MR | Zbl

[3] L. Boutet De Monvel and B. Malgrange, Le théorème de l'indice relatif, Ann. Sci. École Norm. Sup. 23 (1990), 151-192. | DOI | EuDML | Numdam | MR | Zbl

[4] H. Cartan and J. P. Serre, Un théorème de finitude concernant les variétés analytiques compactes, C. R. Acad. Sci. Paris 237 (1953), 128-130. | MR | Zbl

[5] A. D'Agnolo and P. Schapira, La transformée de Radon-Penrose des 𝒟-modules, C. R. Acad. Sci. Paris 319 (1994), 461-466. | MR | Zbl

[6] H. Grauert, Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen, Inst. Hautes Études Sci. Publ. Math. 5 (1960), 233-292. | DOI | EuDML | Numdam | MR | Zbl

[7] C. Houzel, Espaces analytiques relatifs et théorème de finitude, Math. Ann. 205 (1973), 13-54. | DOI | EuDML | MR | Zbl

[8] C. Houzel and P. Schapira, Images directes de modules différentiels, C. R. Acad. Sci. Paris 298 (1984), 461-464. | MR | Zbl

[9] M. Kashiwara, b-functions and holonomic systems, Invent. Math. 38 (1976), 33-53. | DOI | EuDML | MR | Zbl

[10] M. Kashiwara, Systems of microdifferential equations, Progress in Mathematics, no. 34, Birkhäuser, 1983. | MR | Zbl

[11] M. Kashiwara, The Riemann-Hilbert problem for holonomic systems, Publ. Res. Inst. Math. Sci. 20 (1984), 319-365. | DOI | MR | Zbl

[12] M. Kashiwara and P. Schapira, Sheaves on manifolds, Grundlehren der mathematischen Wissenschaften, no. 292, Springer, 1990. | DOI | MR | Zbl

[13] T. Kawai, Finite dimensionality of cohomology groups attached to systems of linear differential equations, J. Math. Kyoto Univ. 13 (1973), 73-95. | DOI | MR | Zbl

[14] Z. Mebkhout, Théorème de dualité globale pour les 𝒟 x -modules cohérents, Math. Scand. 50 (1982), 25-43. | DOI | EuDML | MR | Zbl

[15] J. P. Ramis and G. Ruget, Résidus et dualité, Invent. Math. 26 (1974), 89-131. | DOI | EuDML | MR | Zbl

[16] J. P. Ramis, G. Ruget, and J. L. Verdier, Dualité relative en géométrie analytique complexe, Invent. Math. 13 (1971), 261-283. | DOI | EuDML | MR | Zbl

[17] M. Saito, Induced 𝒟-modules and differential complexes, Bull. Soc. Math. France 117 (1989), 361-387. | DOI | EuDML | Numdam | MR | Zbl

[18] M. Sato, T. Kawai, and M. Kashiwara, Hyperfunctions and pseudo-differential equations, Hyperfunctions and Pseudo-Differential Equations (H. Komatsu, ed.), Lecture Notes in Mathematics, no. 287, Springer, 1973, Proceedings Katata 1971, pp. 265-529. | MR | Zbl

[19] P. Schapira, Microdifferential systems in the complex domain, Grundlehren der mathematischen Wissenschaften, no. 269, Springer, 1985. | DOI | MR | Zbl

[20] P. Schapira, Sheaf theory for partial differential equations, Proceedings of the International Congress of Mathematicians, Kyoto, Springer, 1990. | MR | Zbl

[21] P. Schapira and J.-P. Schneiders, Paires elliptiques I. Finitude et dualité, C. R. Acad. Sci. Paris 311 (1990), 83-86. | MR | Zbl

[22] P. Schapira and J.-P. Schneiders, Elliptic pairs II. Euler class and relative index theorem, this volume. | Numdam | Zbl

[23] J.-P. Schneiders, Un théorème de dualité pour les modules différentiels, C. R. Acad. Sci. Paris 303 (1986), 235-238. | MR | Zbl

[24] J.-P. Schneiders, Dualité pour les modules différentiels, Thèse, Université de Liège, October 1986.

[25] J.-P. Schneiders, A coherence criterion for Fréchet modules, this volume. | Numdam | Zbl

[26] J. P. Serre, Un théorème de dualité, Comm. Math. Helv. 29 (1954), 9-26. | DOI | EuDML | MR | Zbl

[27] M. Zerner, Domaine d'holomorphie des fonctions vérifiant une équation aux dérivées partielles, C. R. Acad. Sci. Paris 272 (1971), 1646-1648. | MR | Zbl