Acta Mathematica

Essential dimension of central simple algebras

Sanghoon Baek and Alexander S. Merkurjev

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Abstract

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.

Article information

Source
Acta Math., Volume 209, Number 1 (2012), 1-27.

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

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485892645

Digital Object Identifier
doi:10.1007/s11511-012-0080-8

Mathematical Reviews number (MathSciNet)
MR2979508

Zentralblatt MATH identifier
1258.16023

Subjects
Primary: 16K50: Brauer groups [See also 12G05, 14F22]
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 20G15: Linear algebraic groups over arbitrary fields

Keywords
Essential dimension Brauer group algebraic tori

Rights
2012 © Institut Mittag-Leffler

Citation

Baek, Sanghoon; Merkurjev, Alexander S. Essential dimension of central simple algebras. Acta Math. 209 (2012), no. 1, 1--27. doi:10.1007/s11511-012-0080-8. https://projecteuclid.org/euclid.acta/1485892645


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