Lectures on the structure of algebraic groups and geometric applications

Includes index

includes Bibliography (p. 111-117)

Machine generated contents note: 1.1.Chevalley's structure theorem 1.2.Rosenlicht decomposition 1.3.Complete homogeneous varieties 1.4.Anti-affine algebraic groups 1.5.Homogeneous vector bundles 1.6.Homogeneous principal bundles 2.1.Criteria for affineness 2.2.Actions of abelian varieties 2.3.Rational actions of algebraic groups 3.1.Some applications 3.2.Rosenlicht decomposition 4.1.Structure 4.2.Blanchard's lemma for group schemes 4.3.Automorphisms 5.1.Characterizations 5.2.Structure 5.3.Semi-abelian varieties 5.4.Extensions by vector groups 5.5.Classification 6.1.Principal bundles 6.2.Equivariant automorphisms 6.3.Automorphisms of vector bundles 6.4.Structure 6.5.Mukai correspondence 7.1.Structure 7.2.Characterizations 7.3.Special classes of principal bundles.

This book originates from a series of 10 lectures given by Professor Michel Brion at the Chennai Mathematical Institute during January 2011. It presents a theorem due to Chevalley on the structure of connected algebraic groups, over algebraically closed fields, as the starting point of various other structure results developed in the recent past.