Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vanishing of cohomology over Cohen--Macaulay rings   A 2003 counterexample to a conjecture of Auslander brought attention to a
family of rings - colloquially called AC rings - that satisfy a natural
condition on vanishing of cohomology. Several results attest to the remarkable
homological properties of AC rings, but their definition is barely operational,
and it remains unknown if they form a class that is closed under typical
constructions in ring theory. In this paper, we study transfer of the AC
property along local homomorphisms of Cohen--Macaulay rings. In particular, we
show that the AC property is preserved by standard procedures in local algebra.
Our results also yield new examples of Cohen-Macaulay AC rings.

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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom