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arXiv · 1008.2406

Essential dimension of simple algebras with involutions

Sanghoon Baek
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Abstract

Let $1\leq m \leq n$ be integers with $m|n$ and $\cat{Alg}_{n,m}$ the class of central simple algebras of degree $n$ and exponent dividing $m$. In this paper, we find new, improved upper bounds for the essential dimension and 2-dimension of $\cat{Alg}_{n,2}$. In particular, we show that $\ed_{2}(\cat{Alg}_{16,2})=24$ over a field $F$ of characteristic different from 2.

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Sanghoon Baek. 2011-04-18. Essential dimension of simple algebras with involutions. https://doi.org/10.1112/blms%2Fbdr120

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