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Cohomology of G/B in characteristic p. (English) Zbl 0612.20023

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.
Reviewer: C.-H.Sah

MSC:

20G10 Cohomology theory for linear algebraic groups
20G05 Representation theory for linear algebraic groups
14L35 Classical groups (algebro-geometric aspects)
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