On the size of the genus of a division algebra

DOI10.1134/S0081543816010053zbMath1356.16013OpenAlexW2964119244MaRDI QIDQ2631142

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

Publication date: 29 July 2016

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543816010053

zbMATH Keywords

division algebraresidue mapunramified Brauer groupdiscrete valuationsfinitely generated field

Mathematics Subject Classification ID

Finite-dimensional division rings (16K20) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Transcendental field extensions (12F20) Brauer groups (algebraic aspects) (16K50) Skew fields, division rings (12E15) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (9)

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 ⋮ Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields ⋮ Spinor groups with good reduction

Uses Software

• RelBrauer

Cites Work

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