2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147162This 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 $p^{2}$ (the result of Deligne-Illusie). The second remark is about the possible relation between adeles and Hodge decomposition. We work out a counter example.AMSLaTeX 1.1, 6 pages, to appear in: Proc. AMS (replaced only to fix a latex problem)Algebraic Geometrytext