Representations of algebraic groups in prime characteristics

DOI10.24033/asens.1397zbMath0466.20017OpenAlexW2597883033MaRDI QIDQ3918293

George R. Kempf

Publication date: 1981

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1981_4_14_1_61_0

zbMATH Keywords

group schemesMumford's conjectureSteinberg representationsconnected reductive grouprational irreducible representationscohomology of sheaves on homogeneous space

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Linear algebraic groups over arbitrary fields (20G15) Representation theory for linear algebraic groups (20G05) Group actions on varieties or schemes (quotients) (14L30) Group schemes (14L15)

Related Items (7)

Cohomology of G/B in characteristic p ⋮ A note on Steinberg modules and Frobenius splitting ⋮ LECTURES ON THE GEOMETRY AND MODULAR REPRESENTATION THEORY OF ALGEBRAIC GROUPS ⋮ Frobenius splitting and hyperplane sections of flag manifolds ⋮ Algebraic groups ⋮ The Steinberg representation ⋮ A Mackey imprimitivity theory for algebraic groups

Cites Work

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• The Frobenius morphism on the cohomology of homogeneous vector bundles on G/B
• A short proof of the Kempf vanishing theorem
• Reductive groups are geometrically reductive
• Linear systems on homogeneous spaces
• The Grothendieck-Cousin complex of an induced representation
• Induced modules and extensions of representations
• Seminar on algebraic groups and related finite groups. Held at the Institute for Advanced Study, Princeton/N.J., 1968/69
• Representations of Algebraic Groups
• Prime Power Representations of Finite Linear Groups II

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