# MathSciDoc: An Archive for Mathematician ∫

#### Quantum AlgebraRings and Algebrasmathscidoc:1701.29002

Acta Mathematica, 209, (1), 1-27, 2010.3
Let\$p\$be a prime integer, 1≤\$s\$≤\$r\$be integers and\$F\$be a field of characteristic different from\$p\$. We find upper and lower bounds for the essential\$p\$-dimension ed_{\$p\$}( \$\$ Al{{g}_{{{{p}^r},{{p}^s}}}} \$\$ ) of the class \$\$ Al{{g}_{{{{p}^r},{{p}^s}}}} \$\$ of central simple algebras of degree\$p\$^{\$r\$}and exponent dividing\$p\$^{\$s\$}. In particular, we show that ed(\$Alg\$_{8,2})=ed_{2}(\$Alg\$_{8,2})=8 and ed_{\$p\$}( \$\$ Al{{g}_{{{{p}^2},p}}} \$\$ )=\$p\$^{2}+\$p\$for\$p\$odd.
Essential dimension; Brauer group; algebraic tori
```@inproceedings{sanghoon2010essential,
title={Essential dimension of central simple algebras},
author={Sanghoon Baek, and Alexander S. Merkurjev},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203358634302756},
booktitle={Acta Mathematica},
volume={209},
number={1},
pages={1-27},
year={2010},
}
```
Sanghoon Baek, and Alexander S. Merkurjev. Essential dimension of central simple algebras. 2010. Vol. 209. In Acta Mathematica. pp.1-27. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203358634302756.