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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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J -invariant of linear algebraic groups

$J$ -invariant of linear algebraic groups