Soient F un corps arbitraire, p un nombre premier positif et D une F-algèbre de division de degré . On écrit pour la variété de Severi–Brauer généralisée des idéaux à droite de dimension réduite , . On note par le motif de Chow à coefficients dans de la variété . Il a été demontré par Nikita Karpenko que ce motif est indecomposable pour tout nombre premier p arbitraire et et pour , . Nous montrons la décomposabilité de dans tous les autres cas.
Let F be an arbitrary field. Let p be a positive prime number and D a central division F-algebra of degree , with . We write for the generalized Severi–Brauer variety of right ideals in D of reduced dimension for . We note by the Chow motive with coefficients in of the variety . It was proven by Nikita Karpenko that this motive is indecomposable for any prime p and and for , . We prove decomposability of in all the other cases.
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@article{CRMATH_2010__348_17-18_989_0, author = {Zhykhovich, Maksim}, title = {Motivic decomposability of generalized {Severi{\textendash}Brauer} varieties}, journal = {Comptes Rendus. Math\'ematique}, pages = {989--992}, publisher = {Elsevier}, volume = {348}, number = {17-18}, year = {2010}, doi = {10.1016/j.crma.2010.07.022}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2010.07.022/} }
TY - JOUR AU - Zhykhovich, Maksim TI - Motivic decomposability of generalized Severi–Brauer varieties JO - Comptes Rendus. Mathématique PY - 2010 SP - 989 EP - 992 VL - 348 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.07.022/ DO - 10.1016/j.crma.2010.07.022 LA - en ID - CRMATH_2010__348_17-18_989_0 ER -
%0 Journal Article %A Zhykhovich, Maksim %T Motivic decomposability of generalized Severi–Brauer varieties %J Comptes Rendus. Mathématique %D 2010 %P 989-992 %V 348 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.07.022/ %R 10.1016/j.crma.2010.07.022 %G en %F CRMATH_2010__348_17-18_989_0
Zhykhovich, Maksim. Motivic decomposability of generalized Severi–Brauer varieties. Comptes Rendus. Mathématique, Tome 348 (2010) no. 17-18, pp. 989-992. doi : 10.1016/j.crma.2010.07.022. http://www.numdam.org/articles/10.1016/j.crma.2010.07.022/
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