Differential operators and the Frobenius pull back of the tangent bundle on \(G/P\)
type: Item
instance of: scholarly article
title: Differential operators and the Frobenius pull back of the tangent bundle on \(G/P\)
zbMATH Open document ID: 0935.14032
author: Niels Lauritzen
author: Vikram B. Mehta
published in: Manuscripta Mathematica
publication date: 2000-05-04T00:00:00Z
review text: The main result of this paper is the following theorem: Let \(G\) be an almost simple, simply connected algebraic group over an algebraically closed field of positive characteristic \(p\). Let \(P\) be a proper parabolic subgroup of \(G\), put \(X:=G/P\) and let \(F\colon X\to X'\) be the Frobenius morphism on \(X\). If \(H^1(X,F^*T_{X'})=0\) (here \(T_{X'}\) denotes the tangent bundle on \(X')\), then \(X\cong {\mathbb P}^n\) for some \(n>0\). This is a generalization of a result of \textit{B. Haastert} [cf. Manuscr. Math. 58, 385-415 (1987; Zbl 0607.14010)]. The present authors use deformation theory and the ``complex geometry'' of \(X\) [cf. \textit{K. H. Paranjape} and \textit{V. Srinivas}, Invent. Math. 98, No. 2, 425-444 (1989; Zbl 0697.14037)] to get their result.
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14G15
Mathematics Subject Classification ID: 14D15
Mathematics Subject Classification ID: 13A35
zbMATH DE Number: 1310842
zbMATH Keywords: algebraic group
zbMATH Keywords: non-vanishing theorems
zbMATH Keywords: flag manifolds
zbMATH Keywords: characteristic \(p\)
zbMATH Keywords: parabolic subgroup
zbMATH Keywords: Frobenius
zbMATH Keywords: tangent bundle
reviewed by: Karl-Heinz Kiyek
MaRDI profile type: Publication
full work available at URL: s002290050157
OpenAlex ID: W2026051240
DOI: 10.1007/S002290050157
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description: scientific article; zbMATH DE number 1310842