Geodesic
Acyclicity versus total acyclicity for complexes over noetherian rings
Documenta mathematica, Tome 11 (2006), pp. 207-240
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It is proved that for a commutative noetherian ring with dualizing complex the homotopy category of projective modules is equivalent, as a triangulated category, to the homotopy category of injective modules. Restricted to compact objects, this statement is a reinterpretation of Grothendieck's duality theorem. Using this equivalence it is proved that the (Verdier) quotient of the category of acyclic complexes of projectives by its subcategory of totally acyclic complexes and the corresponding category consisting of injective modules are equivalent. A new characterization is provided for complexes in Auslander categories and in Bass categories of such rings.
DOI : 10.4171/dm/209
Classification : 13D05, 16E05, 16E10
Mots-clés : totally acyclic complex, dualizing complex, Gorenstein dimension, Auslander category, bass category 
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     author = {Henning Krause and Srikanth Iyengar},
     title = {Acyclicity versus total acyclicity for complexes over noetherian rings},
     journal = {Documenta mathematica},
     pages = {207--240},
     year = {2006},
     volume = {11},
     doi = {10.4171/dm/209},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/209/}
}
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Henning Krause; Srikanth Iyengar. Acyclicity versus total acyclicity for complexes over noetherian rings. Documenta mathematica, Tome 11 (2006), pp. 207-240. doi: 10.4171/dm/209

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