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.
@article{CRMATH_2010__348_17-18_989_0, author = {Maksim Zhykhovich}, 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}, }
Maksim Zhykhovich. Motivic decomposability of generalized Severi–Brauer varieties. Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 989-992. doi : 10.1016/j.crma.2010.07.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.022/
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