Totally Acyclic Approximations

Let Q → R be a surjective homomorphism of Noetherian rings such that Q is Gorenstein and R as a Q -bimodule admits a finite resolution by modules which are projective on both sides. We define an adjoint pair of functors between the homotopy category of totally acyclic R -complexes and that of Q -com...

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Bibliographic Details
Published in:Applied categorical structures 2021-08, Vol.29 (4), p.729-745
Main Authors: Bergh, Petter A., Jorgensen, David A., Moore, W. Frank
Format: Article
Language:English
Subjects:
Approximation
Convex and Discrete Geometry
Geometry
Homomorphisms
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Modules
Rings (mathematics)
Theory of Computation
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Summary:Let Q → R be a surjective homomorphism of Noetherian rings such that Q is Gorenstein and R as a Q -bimodule admits a finite resolution by modules which are projective on both sides. We define an adjoint pair of functors between the homotopy category of totally acyclic R -complexes and that of Q -complexes. This adjoint pair is analogous to the classical adjoint pair of functors between the module categories of R and Q . As a consequence, we obtain a precise notion of approximations of totally acyclic R -complexes by totally acyclic Q -complexes.
ISSN:0927-2852
1572-9095
DOI:10.1007/s10485-021-09633-1