Cohomology of G/B in characteristic p
type: Item
instance of: scholarly article
title: Cohomology of G/B in characteristic p
zbMATH Open document ID: 0612.20023
DOI: 10.1016/0001-8708(86)90050-2
published in: Advances in Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let G be a semisimple algebraic group over an algebraically closed field K of prime characteristic with B denoting a Borel subgroup. There has been a tremendous amount of work done on the relation between the representation theory of G and the cohomology of line bundles on G/B. The present article is a nicely written survey that formulates some conjectures and tentative hypotheses concerning the cohomology in conjunction with some concrete examples. It is pointless to review such articles since all the reviewer can do is to reproduce the article. The article is a recommended reading for experts as well as nonexperts; it is especially recommended for those who would like to enter the field.
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 14L35
zbMATH DE Number: 3989639
zbMATH Keywords: semisimple algebraic group
zbMATH Keywords: Borel subgroup
zbMATH Keywords: representation theory
zbMATH Keywords: cohomology of line bundles
author: James E. Humphreys
reviewed by: Chih-Han Sah
MaRDI profile type: Publication
full work available at URL: 0001-8708(86)90050-2
OpenAlex ID: W2060995955
cites work: Cohomology of line bundles on $G/B$
cites work: The first cohomology group of a line bundle on G/B
cites work: Vanishing theorems and induced representations
cites work: The strong linkage principle.
cites work: On the structure of Weyl modules
cites work: The Frobenius morphism on the cohomology of homogeneous vector bundles on G/B
cites work: On the structure of the cohomology of line bundles on G/B
cites work: Q3947827
cites work: Rational and generic cohomology
cites work: Désingularisation des variétés de Schubert généralisées
cites work: A very simple proof of Bott's theorem
cites work: On Ext1 for semisimple groups and infinitesimal subgroups
cites work: Towards the Kazhdan-Lusztig conjecture
cites work: Cohomology of flag varieties in characteristic p
cites work: A short proof of the Kempf vanishing theorem
cites work: Q4177759
cites work: Q3926788
cites work: The geometry of algebraic groups
cites work: Zur Charakterformel gewisser Darstellungen halbeinfacher Gruppen und Lie-Algebren
cites work: Darstellungen halbeinfacher Gruppen und kontravariante Formen.
cites work: Über das Dekompositionsverhalten gewisser modularer Darstellungen halbeinfacher Gruppen und ihrer Lie-Algebren
cites work: Q3926789
cites work: Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne.
cites work: Representations of Coxeter groups and Hecke algebras
cites work: Q3910633
cites work: Linear systems on homogeneous spaces
cites work: Representations of algebraic groups in prime characteristics
cites work: Geometry of 𝐺/𝑃
cites work: Q3900232
cites work: Hecke algebras and Jantzen's generic decomposition patterns
description: scientific article; zbMATH DE number 3989639