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Essential $ p$-dimension of $ \operatorname{\mathbf{PGL}}(p^2)$


Author: Alexander S. Merkurjev
Journal: J. Amer. Math. Soc. 23 (2010), 693-712
MSC (2010): Primary 16K50, 20G15
Published electronically: January 15, 2010
MathSciNet review: 2629984
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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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Additional Information

Alexander S. Merkurjev
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
Email: merkurev@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-10-00661-2
Keywords: Essential $p$-dimension, Brauer group, algebraic tori.
Received by editor(s): December 8, 2008
Received by editor(s) in revised form: July 12, 2009
Published electronically: January 15, 2010
Additional Notes: The work has been supported by the NSF grant DMS #0652316.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.