Essential 𝑝-dimension of 𝐏𝐆𝐋(𝐩²)

DOI10.1090/S0894-0347-10-00661-2zbMath1231.20048OpenAlexW1969760140MaRDI QIDQ3584360

Alexander S. Merkurjev

Publication date: 27 August 2010

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0894-0347-10-00661-2

zbMATH Keywords

Brauer groupscentral simple algebrasChow groupsessential \(p\)-dimension\(R\)-equivalencecharacter groups of algebraic toriSeveri-Brauer varieties

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Group actions on varieties or schemes (quotients) (14L30) Finite-dimensional division rings (16K20) Brauer groups (algebraic aspects) (16K50)

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Symbol length in the Brauer group of a field, Essential dimension: a survey, Essential dimension of involutions and subalgebras, Essential dimension, \(\mathbb Z_3 \times\mathbb Z_3\) crossed products., Triple Massey products vanish over all fields, Spinors and essential dimension, A lower bound on the essential dimension of PGL₄ in characteristic 2, Essential dimension of simple algebras in positive characteristic., Essential \(p\)-dimension of \(\text{PGL}_n\)., Open problems on central simple algebras.

Cites Work

• Division algebras over Henselian fields.
• Essential dimension of finite \(p\)-groups.
• R-equivalence on three-dimensional tori and zero-cycles
• Essential dimension: A functorial point of view (after A. Merkurjev)
• Prime to \(p\) extensions of division algebras
• La $R$-équivalence sur les tores
• Essential Dimensions of Algebraic Groups and a Resolution Theorem for G-Varieties
• FIELDS OF DEFINITION FOR DIVISION ALGEBRAS
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