Essential 𝑝-dimension of 𝐏𝐆𝐋(𝐩²)

Merkurjev, Alexander

doi:10.1090/S0894-0347-10-00661-2

Essential $p$-dimension of $\operatorname {\mathbf {PGL}}(p^2)$
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by Alexander S. Merkurjev

J. Amer. Math. Soc. 23 (2010), 693-712

DOI: https://doi.org/10.1090/S0894-0347-10-00661-2

Published electronically: January 15, 2010

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Abstract:

Let $p$ be a prime integer and $F$ a field of characteristic different from $p$. We prove that the essential $p$-dimension of the group $\operatorname {\mathbf {PGL}}_F(p^2)$ is equal to $p^2+1$. This integer measures the complexity of the class of central simple algebras of degree $p^2$ over field extensions of $F$.

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