Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A freeness criterion without patching for modules over local rings   It is proved that if $\varphi\colon A\to B$ is a local homomorphism of
commutative noetherian local rings, a nonzero finitely generated $B$-module $N$
whose flat dimension over $A$ is at most $\mathrm{edim}\, A - \mathrm{edim}\,
B$, is free over $B$, and $\varphi$ is a special type of complete intersection.
This result is motivated by a "patching method" developed by Taylor and Wiles,
and a conjecture of de Smit, proved by the first author, dealing with the
special case when $N$ is flat over $A$.

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The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an