Adic semidualizing complexes

Abstract

We introduce and study a class of objects that encompasses Christensen and Foxby's semidualizing modules and complexes and Kubik's quasi-dualizing modules: the class of $\mathfrak{a}$-adic semidualizing modules and complexes. We give examples and equivalent characterizations of these objects, including a characterization in terms of the more familiar semidualizing property. As an application, we give a proof of the existence of dualizing complexes over complete local rings that does not use the Cohen Structure Theorem.

24 pages. now part 5 of a series with arXiv:1401.6925,arXiv:1602.03224, arXiv:1602.03225, arXiv:1602.03226, and arXiv:1602.03227. v.3 is a major revision with shortened title, some material from v.2 has been moved to other papers in this series. comments welcome. v.4 updates references and URL for Sather-Wagstaff