Algebra & Number Theory

A lower bound on the essential dimension of simple algebras

Alexander Merkurjev

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Abstract

Let p be a prime integer and F a field of characteristic different from p. We prove that the essential p-dimension edpCSA(pr) of the class CSA(pr) of central simple algebras of degree pr is at least (r1)pr+1. The integer edpCSA(pr) measures complexity of the class of central simple algebras of degree pr over field extensions of F.

Article information

Source
Algebra Number Theory, Volume 4, Number 8 (2010), 1055-1076.

Dates
Received: 27 November 2009
Revised: 30 March 2010
Accepted: 15 May 2010
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513729609

Digital Object Identifier
doi:10.2140/ant.2010.4.1055

Mathematical Reviews number (MathSciNet)
MR2832634

Zentralblatt MATH identifier
1231.16017

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

Citation

Merkurjev, Alexander. A lower bound on the essential dimension of simple algebras. Algebra Number Theory 4 (2010), no. 8, 1055--1076. doi:10.2140/ant.2010.4.1055. https://projecteuclid.org/euclid.ant/1513729609


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