Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

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

 
 

 

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
DOI: https://doi.org/10.1090/S0894-0347-10-00661-2
Published electronically: January 15, 2010
MathSciNet review: 2629984
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2010): 16K50, 20G15

Retrieve articles in all journals with MSC (2010): 16K50, 20G15


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

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.