Abstract
It is shown that a moduleL over the sheafO of germs of holomorphic functions on a domain G of Cn is injective if and only if the following conditions are satisfied; a)L is flabby; b) for every closed set S ⊂G and every point z λ G, the stalk se z of the sheafS L;U1→Γ S (U:L) is an injectiveO z -module. It follows in particular that the sheaf of germs of hyperfunctions is injective over the sheaf of germs of analytic functions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
A. Grothendieck, “Sur quelques points d'algebre homologique,” Tohoku Math. J.,9, 119–221 (1957).
B. Eckman and A. Schopf, “Über injective Moduln,” Archiv d. Math.,4, No. 2, 75–78 (1953).
S. MacLane, Homology, Springer, Berlin (1963).
P. Shapira, Theory of Hyperfunctions [in Russian], Mir, Moscow (1972).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 18, No. 4, pp. 589–596, October, 1975.
Rights and permissions
About this article
Cite this article
Golovin, V.D. Criteria for the injectivity of analytic sheaves. Mathematical Notes of the Academy of Sciences of the USSR 18, 939–942 (1975). https://doi.org/10.1007/BF01153048
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01153048