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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Essential $p$-dimension of $\operatorname {\mathbf {PGL}}(p^2)$
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by Alexander S. Merkurjev PDF
J. Amer. Math. Soc. 23 (2010), 693-712 Request permission

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 $F$.
References
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Additional Information
  • Alexander S. Merkurjev
  • Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
  • MR Author ID: 191878
  • ORCID: 0000-0002-4447-1838
  • Email: merkurev@math.ucla.edu
  • 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.
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 23 (2010), 693-712
  • MSC (2010): Primary 16K50, 20G15
  • DOI: https://doi.org/10.1090/S0894-0347-10-00661-2
  • MathSciNet review: 2629984