Hübl, Reinhold; Kunz, Ernst Regular differential forms and duality for projective morphisms. (English) Zbl 0709.14014 J. Reine Angew. Math. 410, 84-108 (1990). Let \(f:X\to Y\) be a projective morphism of noetherian excellent separated schemes such that f is equidimensional of dimension d and generically smooth. Let \(\omega^ d_{X/Y}\) be the sheaf of regular differential forms of degree d defined by E. Kunz and R. Waldi in “Regular differential forms”, Contemp. Math. 79 (1988; Zbl 0658.13019). Then an “explicit” duality isomorphism \(f_*{\mathcal H}om_{{\mathcal O}_ X}({\mathcal F},\omega^ d_{X/Y})\overset\sim\rightarrow {\mathcal H}om_{{\mathcal O}_ Y}(R^ df_*{\mathcal F},{\mathcal O}_ Y),\) \({\mathcal F}\in Qcoh(X)\) is constructed for X/Y and a “residue theorem” is proved for X/Y generalizing to the relative case previous absolute results of the second author. Reviewer: A.Buium Cited in 3 ReviewsCited in 8 Documents MSC: 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 13N10 Commutative rings of differential operators and their modules Keywords:sheaf of regular differential forms; duality isomorphism; residue theorem Citations:Zbl 0658.13019 PDFBibTeX XMLCite \textit{R. Hübl} and \textit{E. Kunz}, J. Reine Angew. Math. 410, 84--108 (1990; Zbl 0709.14014) Full Text: DOI Crelle EuDML