arXiv math/01030752001-03math.RAmath.AGmath.RT

Residue Complexes over Noncommutative Rings

Amnon Yekutieli, James J. Zhang

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

英文摘要：

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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