Publications of the Research Institute for Mathematical Sciences

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Volume 12, Issue 99, 1976, pp. 247–256
DOI: 10.2977/prims/1195196607

Published online: 1976-12-31

Local Cohomology of Analytic Spaces

Zoghman Mebkhout[1]

(1) Université Paris 7 Denis Diderot, France

The purpose of this paper is to show that the local cohomology of a complex analytic space embedded in a complex manifold is a holonomic system of linear differential equations of infinite order and its holomorphic solution sheaves are a resolution of the constant sheaf C in this space which provides the Poincaré lemma. The proof relies on the theories of the b-function and holonomic systems due to M. Kashiwara ([2] and [3]) and A. Grothendieck's theorem on the De Rham cohomology of an algebraic variety ([1]). I am very much indebted to M. Kashiwara from whose papers I learned so much.

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Mebkhout Zoghman: Local Cohomology of Analytic Spaces. Publ. Res. Inst. Math. Sci. 12 (1976), 247-256. doi: 10.2977/prims/1195196607