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

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, : XY a proper holomorphic map and T=(T₁,...,T_N) a system of indeterminates. Then, for everyO _XT] graded sheafm, all direct image sheaves R^q_* m areYT]-coherent. The proof is as in 2].

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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.