Essential dimension of finite groups in prime characteristic

Zinovy Reichstein; Angelo Vistoli

doi:10.1016/j.crma.2018.03.013

Algebra

Essential dimension of finite groups in prime characteristic
[Dimension essentielle des groupes finis en caractéristique positive]

Présenté par : Jean-Pierre Serre

Zinovy Reichstein ¹ ; Angelo Vistoli ²

¹ Department of Mathematics, University of British Columbia, Vancouver, B.C., V6T 1Z2, Canada
² Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 463-467.

Résumé
Abstract

Soit F un corps de caractéristique $p > 0$ , et soit G un groupe algébrique fini étale sur F. On calcule la dimension essentielle de G en p, que l'on note ${ed}_{F} (G; p)$ . Plus précisément, on démontre que

{ed}_{F} (G; p) = {\begin{matrix} 1, & si p divise | G |, \\ 0, & sinon. \end{matrix}

Let F be a field of characteristic $p > 0$ and G be a smooth finite algebraic group over F. We compute the essential dimension ${ed}_{F} (G; p)$ of G at p. That is, we show that

{ed}_{F} (G; p) = {\begin{matrix} 1, & if p divides | G |, and \\ 0, & otherwise. \end{matrix}

Reçu le : 2018-01-10
Accepté le : 2018-03-27
Publié le : 2018-04-11

DOI : 10.1016/j.crma.2018.03.013

Affiliations des auteurs :

Zinovy Reichstein ¹ ; Angelo Vistoli ²

¹ Department of Mathematics, University of British Columbia, Vancouver, B.C., V6T 1Z2, Canada
² Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

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     title = {Essential dimension of finite groups in prime characteristic},
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     pages = {463--467},
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     number = {5},
     year = {2018},
     doi = {10.1016/j.crma.2018.03.013},
     language = {en},
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Zinovy Reichstein; Angelo Vistoli. Essential dimension of finite groups in prime characteristic. Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 463-467. doi : 10.1016/j.crma.2018.03.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.03.013/

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Cité par Sources :

^☆ The authors are grateful to the Collaborative Research Group in Geometric and Cohomological Methods in Algebra at the Pacific Institute for the Mathematical Sciences for their support of this project.

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