Open Access
2012 Essential dimension of central simple algebras
Sanghoon Baek, Alexander S. Merkurjev
Author Affiliations +
Acta Math. 209(1): 1-27 (2012). DOI: 10.1007/s11511-012-0080-8


Let p be a prime integer, 1≤sr be integers and F be a field of characteristic different from p. We find upper and lower bounds for the essential p-dimension edp($ Al{{g}_{{{{p}^r},{{p}^s}}}} $) of the class $ Al{{g}_{{{{p}^r},{{p}^s}}}} $ of central simple algebras of degree pr and exponent dividing ps. In particular, we show that ed(Alg8,2)=ed2(Alg8,2)=8 and edp($ Al{{g}_{{{{p}^2},p}}} $)=p2+p for p odd.


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Sanghoon Baek. Alexander S. Merkurjev. "Essential dimension of central simple algebras." Acta Math. 209 (1) 1 - 27, 2012.


Received: 4 March 2010; Revised: 5 July 2010; Published: 2012
First available in Project Euclid: 31 January 2017

zbMATH: 1258.16023
MathSciNet: MR2979508
Digital Object Identifier: 10.1007/s11511-012-0080-8

Primary: 16K50
Secondary: 14L30 , 20G15

Keywords: algebraic tori , Brauer group , Essential dimension

Rights: 2012 © Institut Mittag-Leffler

Vol.209 • No. 1 • 2012
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