Vladimir Chernousov and Alexander Merkurjev : Essential $p$-dimension of split simple groups of type $A_n$

chernous@math.ualberta.ca, merkurev@math.ucla.edu

Submission: 2011, Apr 15

Abstract: We compute the essential $p$-dimension of split simple groups of type $A_{n-1}$ in terms of the functor $\mathit{Alg}(n,m)$ of central simple algebras of degree $n$ and exponent dividing $m$.

2010 Mathematics Subject Classification: 11E72, 16K50, 20G15, 14L30

Keywords and Phrases: Linear algebraic group, torsor, central simple algebra, essential dimension, Brauer group

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