The genus of a division algebra and the unramified Brauer group

DOI10.1007/s13373-013-0037-zzbMath1293.16015arXiv1303.0390OpenAlexW2963479872WikidataQ59304708 ScholiaQ59304708MaRDI QIDQ2844609

Andrei S. Rapinchuk, Igor A. Rapinchuk, Vladimir I. Chernousov

Publication date: 29 August 2013

Published in: Bulletin of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.0390

zbMATH Keywords

Brauer groupscentral simple algebraslinear algebraic groupsquaternion algebrascentral division algebrasmaximal subfieldsmaximal torigenus problemalgebras of exponent two

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Cohomology theory for linear algebraic groups (20G10) Finite-dimensional division rings (16K20) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Brauer groups (algebraic aspects) (16K50) Skew fields, division rings (12E15)

Related Items (11)

Examples of algebraic groups of type \(G_2\) having the same maximal tori ⋮ On the size of the genus of a division algebra ⋮ Division algebras of prime degree with infinite genus ⋮ On some finiteness properties of algebraic groups over finitely generated fields ⋮ Division algebras with common subfields ⋮ The finiteness of the genus of a finite-dimensional division algebra, and some generalizations ⋮ Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction ⋮ A finiteness theorem for special unitary groups of quaternionic skew-Hermitian forms with good reduction ⋮ Linear algebraic groups with good reduction ⋮ The norm principle for type $D_n$ groups over complete discretely valued fields ⋮ Spinor groups with good reduction

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