The Action of Adeles on the Residue Complex

Details The Action of Adeles on the Residue Complex The Action of Adeles on the Residue Complex

2002-05-02

arxiv.org/abs/math/0205018v2

Mathematics

Algebraic Geometry

19 pages, LaTeX with xypic package; final version, to appear in Comm. Algebra (Steven Kleiman issue)

Scientific paper

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.

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