Essential dimension of central simple algebras

Sanghoon Baek Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology Alexander S. Merkurjev Department of Mathematics, University of California, Los Angeles

Quantum Algebra Rings and Algebras mathscidoc: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
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  title={Essential dimension of central simple algebras},
  author={Sanghoon Baek, and Alexander S. Merkurjev},
  booktitle={Acta Mathematica},
Sanghoon Baek, and Alexander S. Merkurjev. Essential dimension of central simple algebras. 2010. Vol. 209. In Acta Mathematica. pp.1-27.
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