Some observations on cohomologically \(p\)-ample bundles
type: Item
instance of: scholarly article
title: Some observations on cohomologically \(p\)-ample bundles
zbMATH Open document ID: 0797.14008
DOI: 10.1007/BF01759316
author: Luca Migliorini
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1994-02-24T00:00:00Z
review text: The author obtains a vanishing theorem for the cohomology of a \(p\)-ample bundle. A key step is the use of a result of \textit{P. Deligne} and \textit{L. Illusie} which gives an algebraic proof of the Kodaira-Akizuki-Nakano vanishing theorem [Invent. Math. 89, 247-270 (1987; Zbl 0632.14017)]. It is proved that no projective scheme of dimension greater than 1, liftable over \(W_ 2(k)\), has cohomologically \(p\)-ample cotangent bundle. There are discussed the cohomologically \(p\)-ample bundles on \(\mathbb{P}^ d_{F_ p}\). There are obtained sufficient conditions for a Frobenius morphism not to be extended to any lifting of a projective \(X\) to \(W_ 2 (k)\).
reviewed by: Doru Ştefănescu
Mathematics Subject Classification ID: 14F17
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14F30
zbMATH DE Number: 495895
zbMATH Keywords: \(p\)-ample bundle
zbMATH Keywords: vanishing theorem
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01759316
OpenAlex ID: W2318532821
description: scientific article; zbMATH DE number 495895