We develop in this paper the stable theory for projective complexes, by which we mean to consider a chain complex of finitely generated projective modules as an object of the factor category of the homotopy category modulo split complexes. As a result of the stable theory we are able to prove that any complex of finitely generated projective modules over a generically Gorenstein ring is acyclic if and only if its dual complex is acyclic. This shows the dependence of total reflexivity conditions for modules over a generically Gorenstein ring.
MSC Codes 13D02, 18G35
|Publication status||Published - May 15 2018|
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