Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variants of normality for Noetherian schemes   This note presents a uniform treatment of normality and three of its
variants---topological, weak and seminormality---for Noetherian schemes. The
key is to define these notions for pairs $(Z, X)$ consisting of a (not
necessarily reduced) scheme $X$ and a closed, nowhere dense subscheme $Z$. An
advantage of the new definitions is that, unlike the usual absolute ones, they
are preserved by completions. This shortens some of the proofs and leads to
more general results. Version 2: small changes.

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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: physics