2002/05/02 by Amnon Yekutieli, Yekutieli, Amnon
Mathematics · #14F05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:14F05
paper · pdf · doi:10.48550/arxiv.math/0205018
19 pages, LaTeX with xypic package; final version, to appear in Comm. Algebra (Steven Kleiman issue)
openalex publication_date 2002/05/02 · arxiv created 2002/07/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a scheme of finite type over a perfect field k. In this paper we study the relation between two important objects associated to X: the Grothendieck residue complex and the Beilinson adeles complex. It is known that the complex of adeles is a DGA (differential graded algebra). Our first main result is that the residue complex is a right DG module over the adeles complex. The second main result is that the de Rham residue complex is a DG module over the de Rham adeles complex. This action gives rise to the cap product in de Rham (co)homology.