Title: Residue Complexes over Noncommutative Rings
Authors: Amnon Yekutieli and James J. Zhang

Publication status: Journal of Algebra 259 (2003) 451–493. 

Abstract:
Residue complexes were introduced by Grothendieck in algebraic
geometry. These are canonical complexes of injective modules that
enjoy remarkable functorial properties (traces).

In this paper we study residue complexes over noncommutative
rings. These objects are even more complicated than in the
commutative case, since they are complexes of bimodules. We
develop methods to prove uniqueness, existence and functoriality
of residue complexes.

For a noetherian affine PI algebra over a field (admitting a
noetherian connected filtration) we prove existence of the residue
complex and describe its structure in detail.
 

Errata:

• There is a mistake in the proof of Lemma 1.24. (This was noticed by Rishi Vyas.) The lemma is correct if the base ring K is assumed to be a field (the proof has to be changed slightly). Thus Theorem 1.23 is only known to be true when K is a field. This is not too bad, since from Section 3 onward this is the assumption anyhow.

• In Lemma 4.11 (and therefore also in Lem 4.12) it is probably necesssary to assume that A is 2-sided noetherian. The correct reference is [GW 2nd Ed, Prop 7.19]. [Reported by R. Vyas]

• "Proof of Thm 4.8" should be changed to "Proof of Thm 4.10". [Reported by R. Vyas]

Electronic Preprint:

• amslatex file with XYpic figures 

• postscript file   

• Eprint math.RA/0103075 at arXiv. 

Journal format (pdf)  

updated 26 Jan 2015