On Gorenstein injective discrete modules over profinite groups |
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Authors: | Edgar Enochs J R García Rozas Luis Oyonarte Blas Torrecillas |
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Institution: | 1. Dept. of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA 2. Dept. de álgebra y Análisis Matemático, Universidad de Almería, 04071, Almería, Spain
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Abstract: | Gorenstein homological algebra was introduced in categories of modules. But it has proved to be a fruitful way to study various other categories such as categories of complexes and of sheaves. In this paper, the research of relative homological algebra in categories of discrete modules over profinite groups is initiated. This seems appropriate since (in some sense) the subject of Gorenstein homological algebra had its beginning with Tate homology and cohomology over finite groups. We prove that if the profinite group has virtually finite cohomological dimension then every discrete module has a Gorenstein injective envelope, a Gorenstein injective cover and we study various cohomological dimensions relative to Gorenstein injective discrete modules. We also study the connection between relative and Tate cohomology theories. |
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