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Cohomology, Maximal Ideals, and Point Evaluations

Alexander Nagel
Proceedings of the American Mathematical Society
Vol. 42, No. 1 (Jan., 1974), pp. 47-50
DOI: 10.2307/2039675
Stable URL: http://www.jstor.org/stable/2039675
Page Count: 4
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Cohomology, Maximal Ideals, and Point Evaluations
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Abstract

We consider algebras A of continuous complex valued functions, which are given as the set of global sections of a sheaf I on a topological space X. Under the hypothesis that all the higher cohomology groups of the sheaf are zero, we investigate the relationship between ideals in A, kernels of algebra homomorphisms of A into the complex numbers C, and sets of functions vanishing at a point of X. As applications, we obtain some simple proofs of theorems about ideals in certain algebras of holomorphic functions.

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