# Séminaires : Séminaire Théorie des Nombres

 Equipe(s) : tn, Responsables : Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos Email des responsables : ziyang.gao@imj-prg.fr Salle : Adresse : Description http://www.imj-prg.fr/tn/STN/stnj.html

 Orateur(s) Kirill Zainoulline - , Titre J-invariant of an algebraic group Date 18/12/2006 Horaire 14:00 à 16:00 Résume Let $G$ be a linear algebraic group over a field $F$ and $X$ be aprojective homogeneous $G$-variety such that $G$ splitsover the function field of $X$.We introduce an invariant of $G$ called $J$-invariantwhich characterizes the splitting properties of the Chow motive of $X$.As a main application we obtain a uniform proof ofall known motivic decompositions of generically splitprojective homogeneous varieties(Severi-Brauer varieties, Pfister quadrics, maximal orthogonalGrassmannians,$G_2$- and $F_4$-varieties)as well as provide new ones (exceptional varieties of types$E_6$, $E_7$ and $E_8$).We also discuss applications totorsion indices, canonical dimensionsand splitting properies of the group $G$. Salle Adresse