Comptes Rendus
Algebra
Essential dimension of simple algebras in positive characteristic
[Dimension essentielle des algèbres simples en caractéristique positive]
Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 375-378.

Soit p un nombre premier. Pour toutes nombres entiers 1sr, on note pr,ps la classe des algèbres simples centrales de degré pr et dʼexposant au plus ps. Pour tous s<r, nous trouvons une borne inférieure pour la p-dimension essentielle de pr,ps. De plus, nous calculons une borne supérieure pour 8,2 sur un corps de caractéristique 2. En conséquence, on montre que ed2(4,2)=ed(4,2)=3 et 3ed(8,2)10 sur un corps de caractéristique 2.

Let p be a prime integer. For any integers 1sr, pr,ps denotes the class of central simple algebras of degree pr and exponent dividing ps. For any s<r, we find a lower bound for the essential p-dimension of pr,ps. Furthermore, we compute an upper bound for 8,2 over a field of characteristic 2. As a result, we show ed2(4,2)=ed(4,2)=3 and 3ed(8,2)10 over a field of characteristic 2.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2011.03.014

Sanghoon Baek 1

1 Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, ON K1N6N5, Canada
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Sanghoon Baek. Essential dimension of simple algebras in positive characteristic. Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 375-378. doi : 10.1016/j.crma.2011.03.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.03.014/

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