Essential dimension of simple algebras in positive characteristic

Sanghoon Baek

doi:10.1016/j.crma.2011.03.014

Algebra

Essential dimension of simple algebras in positive characteristic

the Editorial Board

Sanghoon Baek ¹

¹Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, ON K1N6N5, Canada

Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 375-378

Abstract (Original language)
Résumé

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

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

Article information
Cite this article

Received: 2011-01-18
Accepted: 2011-03-15
Published online: 2011-04-01

DOI: 10.1016/j.crma.2011.03.014

Author's affiliations:

Sanghoon Baek ¹

¹ Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, ON K1N6N5, Canada

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

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