1996/02/14 by Amnon Yekutieli, Yekutieli, Amnon · 1 citation
Mathematics · #13N05 (Secondary) #14B10 #14F10 (Primary) 14F40 #14F32 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #alg-geom #math.AC #math.AG #msc:13N05 #msc:14B10 #msc:14F10 #msc:14F32 #msc:14F40
paper · pdf · doi:10.48550/arxiv.alg-geom/9602011
35 pages, AMSLaTeX, final version (minor changes), to appear in Duke Math. J
openalex publication_date 1996/02/14 · arxiv created 1998/02/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.