Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gorenstein dimensions of unbounded complexes and faithfully flat change
  of base (With an appendix by Driss Bennis)   For a commutative ring R and a faithfully flat R-algebra S we prove, under
mild extra assumptions, that an R-module M is Gorenstein flat if and only if
the left S-module S\otimes M is Gorenstein flat, and that an R-module N is
Gorenstein injective if and only if it is cotorsion and the left S-module
Hom(S,N) is Gorenstein injective. We apply these results to the study of
Gorenstein homological dimensions of unbounded complexes. In particular, we
prove two theorems on stability of these dimensions under faithfully flat
(co-)base change.

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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas