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

Benjamin Antieau; Gabriele Vezzosi

doi:10.2422/2036-2145.201711_007

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

Benjamin Antieau, Gabriele Vezzosi

Mathematics

Research output: Contribution to journal › Article › peer-review

10 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 language	English (US)
Pages (from-to)	1135-1145
Number of pages	11
Journal	Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume	20
Issue number	3
DOIs	https://doi.org/10.2422/2036-2145.201711_007
State	Published - 2020

Funding

Benjamin Antieau was supported by NSF Grant DMS-1552766.

ASJC Scopus subject areas

Theoretical Computer Science
Mathematics (miscellaneous)

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AB - 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.

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

Abstract

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