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Le complete formel d'un espace analytique le long d'un sous-espace: Un theoreme de comparaison

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Abstract

We prove here a theorem, which generalizes Grauert's comparison theorem ([4], Hauptsatz IIa; cf. also Knorr [7], Vergleichssatz) and which is an analogue of a Grothéndieck's result in Algebraic Geometry ([6], Chap. III., 4.1.5). The proof makes essential use of a coherence theorem for sheaves of polynomials: Let X,Y be complex spaces, π: X→Y a proper holomorphic map and T=(T1,...,TN) a system of indeterminates. Then, for everyO X[T] graded sheafm, all direct image sheaves Rqπ* m areY[T]-coherent. The proof is as in [2].

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Bibliographie

  1. H. CARTAN: Familles d'espaces complexes et fondements de la géométrie analytique. Séminaire E.N.S. Paris (1960–61).

  2. O. FORSTER und K. KNORR: Ein Beweis des Grauertschen Bildgarbensatzes nach Ideen von B. Malgrange. Manuscripta math. 5, 19–44 (1971).

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  3. J. FRISCH: Points de platitude d'un morphisme d'espaces analytiques complexes. Inventiones Math., 4, 118–138 (1967).

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  4. H. GRAUERT: Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen. Publ. Math. I.H.E.S. no5, Paris (1960).

  5. A. GROTHENDIECK: Espaces vectoriels topologiques. Departamento de Matemática da Universidade de Sao Paulo (1954).

  6. A. GROTHENDIECK: Eléments de géométrie algébrique, Chap. I et III, Publ. Math. I.H.E.S. no4 et no11, Paris (1960–1961).

  7. K. KNORR: Der Grauertsche Projektionssatz. Inventiones Math. 12, 118–172 (1971).

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  8. G. KÖTHE: Über zwei Sätze von Banach, Math. Z. 53, 203–209 (1950).

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Diese Arbeit entstand während eines Aufenthalts des Verfassers am Fachbereich Mathematik der Universität Regensburg als Stipendiat der Alexander-von-Humboldt-Stiftung.

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Banica, C. Le complete formel d'un espace analytique le long d'un sous-espace: Un theoreme de comparaison. Manuscripta Math 6, 207–244 (1972). https://doi.org/10.1007/BF01304612

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  • DOI: https://doi.org/10.1007/BF01304612

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