Relations between semidualizing complexes (Q847967)

Let \(B\) and \(C\) be semidualizing complexes over commutative noetherian ring \(R\). The paper concerns with a version of \textit{L. L. Avramov, R.-O. Buchweitz} and \textit{L. M. Şega}'s question [J.\ Pure Appl.\ Algebra 201, No.\ 1--3, 218--239 (2005; Zbl 1087.13010)]: Does the vanishing of \(\mathrm{Ext}^n_R(B,C)\) for \(n\gg 0\) imply that \(B\) is \(C\)-reflexive? The results come in three types: (1) Assuming \(\mathrm{Ext}^n_R(B,C)=0\) for \(n\gg 0\) and a bit more, \(B\) is \(C\)-reflexive; (2) Write \([B]\approx[C]\) if there is a tiling \(R\)-complex \(P\) with \(B\cong\otimes^L_R C\). Assuming \(\mathrm{Ext}^n_R(B,C)=0\) for \(n\gg 0\) and a lot more, \([B]\approx [C]\) is deduced; (3) Analogues of results of Avramov, Buchweitz and Şega are presented.