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A central extension theorem for essential dimensions

Author(s): Ming-Chang Kang
Journal: Proc. Amer. Math. Soc. 136 (2008), 809-813.
MSC (2000): Primary 12E05, 12F10, 12F20, 13F30
Posted: November 28, 2007
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Abstract: Let $ K$ be an arbitrary field and $ G$ a finite group. We will denote by $ \operatorname{ed}_K(G)$ the essential dimension of $ G$ over $ K$. A generalization of the central extension theorem of Buhler and Reichstein (Compositio Math. 106 (1997) 159-179, Theorem 5.3) is obtained.

References:

[BF]
G. Berhuy and G. Favi, Essential dimension: a functorial point of view after A. Merkurjev, Documenta Math. 8 (2003), 279-330. MR 2029168 (2004m:11056)

[Bo]
N. Bourbaki, Commutative algebra, Hermann, Paris, 1972. MR 0360549 (50:12997)

[BR]
J. Buhler and Z. Reichstein, On the essential dimension of a finite group, Compositio Math. 106 (1997), 159-179. MR 1457337 (98e:12004)

[JLY]
C. Jensen, A. Ledet and N. Yui, Generic polynomials: constructive aspects of the inverse Galois problem, MSRI Publ. vol. 45, Cambridge University Press, Cambridge, 2002. MR 1969648 (2004d:12007)

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Additional Information:

Ming-Chang Kang
Affiliation: Department of Mathematics, National Taiwan University, Taipei, Taiwan
Email: kang@math.ntu.edu.tw

DOI: 10.1090/S0002-9939-07-09078-8
PII: S 0002-9939(07)09078-8
Keywords: Essential dimension, Galois theory, group actions, valuation rings
Received by editor(s): November 28, 2006
Posted: November 28, 2007
Communicated by: Martin Lorenz
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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