Algebra & Number Theory

Essential dimension of spinor and Clifford groups

Vladimir Chernousov and Alexander Merkurjev

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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

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

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

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Zentralblatt MATH identifier

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

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


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.

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