Some Remarks on Beilinson Adeles

1995/10/05 by Amnon Yekutieli, Yekutieli, Amnon
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9510006

AMSLaTeX 1.1, 6 pages, to appear in: Proc. AMS (replaced only to fix a latex problem)

openalex publication_date 1995/10/05 · arxiv created 1995/10/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper contains two remarks on Beilinson's adeles with values in the De Rham complex of a scheme. The first is an interpretation, in terms of adeles, of the decomposition of the De Rham complex on a scheme defined modulo p² (the result of Deligne-Illusie). The second remark is about the possible relation between adeles and Hodge decomposition. We work out a counter example.

Related

• The Action of Adeles on the Residue Complex
• Model Theory of Adeles and Number Theory
• Adelic descent for K-theory
• Beilinson-Parshin adeles via solid algebraic geometry
• The Hodge theory of the Decomposition Theorem (after de Cataldo and Migliorini)