Holomorphic convexity of compact sets in analytic spaces and the structure of algebras of holomorphic germs

Zame, William R.

doi:10.1090/S0002-9947-1976-0425179-8

Holomorphic convexity of compact sets in analytic spaces and the structure of algebras of holomorphic germs
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Trans. Amer. Math. Soc. 222 (1976), 107-127 Request permission

Abstract:

Let $(X,{\mathcal {O}_X})$ be a reduced analytic space and let K be a compact, holomorphically convex subset of X. It is shown that analogs of Cartan’s Theorems A and B are valid for coherent analytic sheaves on K. This result is applied to the study of the algebra of germs on K of functions holomorphic near K. In particular, characterizations of finitely generated ideals, prime ideals and homomorphisms are obtained.

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Convexity and approximation in Stein spaces

William R. Zame, Algebras of analytic germs, Trans. Amer. Math. Soc. 174 (1972), 275–288. MR 313545, DOI 10.1090/S0002-9947-1972-0313545-7
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Ideals in rings of holomorphic germs

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Holomorphic convexity of compact sets and cohomology vanishing theorems

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