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J -invariant of linear algebraic groups

Viktor Petrov, Nikita Semenov, Kirill Zainoulline (2008)

Annales scientifiques de l'École Normale Supérieure

Let G be a semisimple linear algebraic group of inner type over a field F , and let X be a projective homogeneous G -variety such that G splits over the function field of X . We introduce the J -invariant of G which characterizes the motivic behavior of X , and generalizes the J -invariant defined by A. Vishik in the context of quadratic forms. We use this J -invariant to provide motivic decompositions of all generically split projective homogeneous G -varieties, e.g. Severi-Brauer varieties, Pfister quadrics,...

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