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
[Dimension essentielle des algèbres simples en caractéristique positive]

Présenté par : the Editorial Board

Sanghoon Baek ¹

¹ Department 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.

Résumé
Abstract

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.

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.

Reçu le : 2011-01-18
Accepté le : 2011-03-15
Publié le : 2011-04-01

DOI : 10.1016/j.crma.2011.03.014

Affiliations des auteurs :

Sanghoon Baek ¹

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

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     title = {Essential dimension of simple algebras in positive characteristic},
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     pages = {375--378},
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     number = {7-8},
     year = {2011},
     doi = {10.1016/j.crma.2011.03.014},
     language = {en},
}

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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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