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 ( and ) and A. Grothendieck's theorem on the De Rham cohomology of an algebraic variety (). I am very much indebted to M. Kashiwara from whose papers I learned so much.
Cite this article
Zoghman Mebkhout, Local Cohomology of Analytic Spaces. Publ. Res. Inst. Math. Sci. 12 (1976), no. 99, pp. 247–256DOI 10.2977/PRIMS/1195196607