Algebra & Number Theory

Essential dimension of spinor and Clifford groups

Vladimir Chernousov and Alexander Merkurjev

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Abstract

We conclude the computation of the essential dimension of split spinor groups, and an application to algebraic theory of quadratic forms is given. We also compute essential dimension of the split even Clifford group or, equivalently, of the class of quadratic forms with trivial discriminant and Clifford invariant.

Article information

Source
Algebra Number Theory, Volume 8, Number 2 (2014), 457-472.

Dates
Received: 27 March 2013
Revised: 25 May 2013
Accepted: 24 June 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730157

Digital Object Identifier
doi:10.2140/ant.2014.8.457

Mathematical Reviews number (MathSciNet)
MR3212863

Zentralblatt MATH identifier
1312.11024

Subjects
Primary: 11E04: Quadratic forms over general fields 11E57: Classical groups [See also 14Lxx, 20Gxx] 11E72: Galois cohomology of linear algebraic groups [See also 20G10]
Secondary: 11E81: Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24] 14L35: Classical groups (geometric aspects) [See also 20Gxx, 51N30] 20G15: Linear algebraic groups over arbitrary fields

Keywords
Linear algebraic groups spinor groups essential dimension torsor nonabelian cohomology quadratic forms Witt rings the fundamental ideal

Citation

Chernousov, Vladimir; Merkurjev, Alexander. Essential dimension of spinor and Clifford groups. Algebra Number Theory 8 (2014), no. 2, 457--472. doi:10.2140/ant.2014.8.457. https://projecteuclid.org/euclid.ant/1513730157


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