2016/06/25 by Petter A. Bergh, Bergh, Petter A., David A. Jorgensen +3
Mathematics · #13C14 #13D02 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C14 #msc:13D02 #msc:13H10
paper · pdf · doi:10.48550/arxiv.1606.07976
arxiv created 2016/06/25 · arxiv updated 2016/06/28
Let R be a commutative local ring. We study the subcategory of the homotopy category of R-complexes consisting of the totally acyclic R-complexes. In particular, in the context where Q→ R is a surjective local ring homomorphism such that R has finite projective dimension over Q, we define an adjoint pair of functors between the homotopy category of totally acyclic R-complexes and that of Q-complexes, which are analogous to the classical adjoint pair between the module categories of R and Q. We give detailed proofs of the adjunction in terms of the unit and counit. As a consequence, one obtains a precise notion of approximations of totally acyclic R-complexes by totally acyclic Q-complexes.