Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Gross-Kuz'min Connjecture for CM fields   Let $A' = \varprojlim_n A'_n$ be the projective limit of the $p$-parts of the
ideal class groups of the $p$ integers in the $\mathbb{Z}_p$-cyclotomic
extension $K_{\infty}/K$ of a CM number field $K$. We prove in this paper that
the $T$-part $(A')^-(T) = \{ 1 \}$ for CM extensions $K/\mathbb{Q}$. This fact
has been conjectured for arbitrary fields $K$ by Kuz'min in 1972 and was proved
by Greenberg in 1973, for abelian extensions $K/\mathbb{Q}$. Federer and Gross
had shown in 1981 that $(A')^-(T) = \{ 1 \}$ is equivalent to the non-vanishing
of the $p$-adic regulator of the $p$-units of $K$.

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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int