Complete Homology over associative rings

Abstract

We compare two generalizations of Tate homology: stable homology and the J-completion of Tor, also known as complete homology. For finitely generated modules, we show that the two theories agree over Artin algebras and over commutative noetherian rings that are Gorenstein, or local and complete.

Updated after referee report: Title expanded; added appendix on comparison map; old Example 2.7 was flawed and has been replaced by Question A.5; minor editorial changes. Final version, to appear in Israel J. Math.; 17 pp