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Regular differential forms and duality for projective morphisms. (English) Zbl 0709.14014

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

MSC:

14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
13N10 Commutative rings of differential operators and their modules

Citations:

Zbl 0658.13019
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