Lundqvist, Johannes A local Grothendieck duality for Cohen-Macaulay ideals. (English) Zbl 1276.32002 Math. Scand. 111, No. 1, 42-52 (2012). In an important paper [Ann. Sci. Éc. Norm. Supér. (4) 40, No. 6, 985–1007 (2007; Zbl 1143.32003)] M. Andersson and E. Wulcan constructed for any coherent sheaf of ideals \(\mathcal{J}\) locally a vector-valued residue current \(R\) whose annihilator is precisely \(\mathcal{J}\). If \(\mathcal{J}\) is a complete intersection, then \(R\) is just the classical Coleff-Herrera product and the statement comes down to the classical Grothendieck duality theorem (see also [A. Dickenstein and C. Sessa, Invent. Math. 80, 417–434 (1985; Zbl 0556.32005)] and [M. Passare, Math. Scand. 62, No. 1, 75–152 (1988; Zbl 0633.32005)].In the paper under review, Lundqvist gives a new proof of the result of Andersson and Wulcan in case \(\mathcal{J}\) is Cohen-Macaulay. This proof has the advantage that it does not require Hironaka’s resolution of singularities and provides a semi-explicit realization of the residue annihilating \(\mathcal{J}\). Reviewer: Jean Ruppenthal (Wuppertal) Cited in 5 Documents MSC: 32A10 Holomorphic functions of several complex variables 32A27 Residues for several complex variables 32C30 Integration on analytic sets and spaces, currents 32C37 Duality theorems for analytic spaces 32A60 Zero sets of holomorphic functions of several complex variables Keywords:coherent ideal sheaf; annihilator; Cohen-Macaulay ideal; Coleff-Herrera current; local Grothendieck duality Citations:Zbl 1143.32003; Zbl 0556.32005; Zbl 0633.32005 PDFBibTeX XMLCite \textit{J. Lundqvist}, Math. Scand. 111, No. 1, 42--52 (2012; Zbl 1276.32002) Full Text: DOI arXiv