Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Peak Point Theorem for Uniform Algebras on Real-Analytic Varieties   It was once conjectured that if $A$ is a uniform algebra on its maximal ideal
space $X$, and if each point of $X$ is a peak point for $A$, then $A = C(X)$.
This peak-point conjecture was disproved by Brian Cole in 1968. Here we
establish a peak-point theorem for uniform algebras generated by real-analytic
functions on real-analytic varieties, generalizing previous results of the
authors and John Wermer.

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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph