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The Action of Adeles on the Residue Complex

Amnon Yekutieli
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Abstract

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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Amnon Yekutieli. 2002-07-24. The Action of Adeles on the Residue Complex. https://arxiv.org/abs/math/0205018

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