Residues and Differential Operators on Schemes

Details Residues and Differential Operators on Schemes Residues and Differential Operators on Schemes

1996-02-14

arxiv.org/abs/alg-geom/9602011v2

Mathematics

Commutative Algebra

35 pages, AMSLaTeX, final version (minor changes), to appear in Duke Math. J

Scientific paper

Beilinson Completion Algebras (BCAs) are generalizations of complete local rings, and have a rich algebraic-analytic structure. These algebras were introduced in my paper "Traces and Differential Operators over Beilinson Completion Algebras", Compositio Math. 99 (1995). In the present paper BCAs are used to give an explicit construction of the Grothendieck residue complex on an algebraic scheme. This construction reveals new properties of the residue complex, and in particular its interaction with differential operators. Applications include: (i) results on the algebraic structure of rings of differential operators; (ii) an analysis of the niveau spectral sequence of De Rham homology; (iii) a proof of the contravariance of De Rham homology w.r.t. etale morphisms; (iv) an algebraic description of the intersection cohomology D-module of a curve.

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