Some remarks on Beilinson adeles

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Let X be a scheme of finite type over a field k. Denote by Aẋ the sheaf of Beilinson adeles with values in the algebraic De Rham complex ΩX/k̇. Then ΩX/k̇ → Aẋ is a flasque resolution. So if X is smooth, Aẋ calculates De Rham cohomology. In this note we rewrite the proof of Deligne-Illusie for the degeneration of the Hodge spectral sequence in terms of adeles. We also give a counterexample to show that the filtration AẊ,≥q does not induce Hodge decomposition.

Original languageEnglish
Pages (from-to)3613-3618
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number12
StatePublished - 1 Jan 1996
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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