A remark on the Hochschild-Kostant-Rosenberg theorem in characteristic p

Benjamin Antieau, Gabriele Vezzosi

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We prove a Hochschild-Kostant-Rosenberg decomposition theorem for smoothly compactifiable smooth schemes X in characteristic p when dim X ≤ p. The best known previous result of this kind, due to Yekutieli, required dim X < p. Yekutieli's result follows fromthe observation that the denominators appearing in the classical proof of HKR do not divide p when dim X < p. Our extension to dim X = p requires a homological fact: the Hochschild homology of a smooth proper scheme is self-dual.

Original languageEnglish (US)
Pages (from-to)1135-1145
Number of pages11
JournalAnnali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume20
Issue number3
DOIs
StatePublished - 2020

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)

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