Essential dimension of simple algebras with involutions

Details Essential dimension of simple algebras with involutions Essential dimension of simple algebras with involutions

2010-08-14

arxiv.org/abs/1008.2406v5

Mathematics

Rings and Algebras

Sections 1 and 3 are rewritten

Scientific paper

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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