**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.

**Errat****a:**

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:**

Eprint math.RA/0103075 at arXiv.

**Journal
format**
(pdf)

updated 26 Jan 2015