Residue Complexes over Noncommutative Rings

Details Residue Complexes over Noncommutative Rings Residue Complexes over Noncommutative Rings

2001-03-13

arxiv.org/abs/math/0103075v3

Mathematics

Rings and Algebras

37 pages, AMSLaTeX with XYpic figures; some changes in Section 3; final version, to appear in Algebr. Represent. Theory

Scientific paper

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.

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