Generically split projective homogeneous varieties

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Table of contents

I Introduction
II Basic material 
II.1 Denition and basic properties of Chow groups
II.2 Further properties of Chow groups
II.3 Steenrod operations on Chow groups modulo 2
II.4 Grothendieck rings
III Quadrics 
III.1 Decomposition on Chow groups of projective quadrics
III.2 Rationality on Chow groups modulo 2 – Main result
III.3 Rationality on Chow groups modulo 2 – Other results
III.4 Rationality on integral Chow groups – Main version
III.5 Rationality on integral Chow groups – A stronger version
IV Exceptional projective homogeneous varieties 
IV.1 Filtrations on Grothendieck ring of projective homogeneous varieties
IV.2 Generically split projective homogeneous varieties
IV.3 J-invariant
IV.4 Proof of the result
V Principal homogeneous space for SL1(A) 
V.1 Preliminaries
V.2 Proof of the result
V.3 Link with Chapter IV – Exceptional projective homogeneous varieties
VI Special correspondences 
VI.1 A conjecture of A. Vishik
VI.2 Rationality of special correspondences on quadrics
VI.3 A partial answer to the conjecture
VI.4 Special correspondences on A-trivial varieties
A Milnor K-Theory 
B Chern classes 
C Correspondences on Chow groups 
D Torsors of algebraic groups 
Bibliography