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- Page 1. Ž . JOURNAL OF ALGEBRA 186, 522543 1996 ARTICLE NO. 0385 The Residue Complex of a Noncommutative Graded Algebra Amnon Yekutieli* Department of Theoretical Mathematics, The Weizmann Institute of Science, Reho¨ot 76100, Israel Communicated by JT Stafford Received November 1, 1995 DEDICATED TO THE MEMORY OF PROFESSOR SHIMSHON AMITSUR 0. INTRODUCTION Suppose A is a finitely generated commutative algebra over a field k. According to Grothendieck duality theory, there is a canonical complex K A of A-modules, called the residue complex. It is characterized as the Cousin complex of the twisted inverse image ! k, where : X s Spec A ª k is the structural morphism. K has the decomposition A Kyq s K x 0.1 Ž . Ž . [ A A xgX rX q qy1 Ž . where X rX : X is the set of points of dimension q the q-skeleton q qy1 Ž . Ž . and K x is an injective hull of the residue field kx …