Linkage of Symbol p-Algebras of Degree 3

2019/01/02 by Adam Chapman, Chapman, Adam
Mathematics · #11E04 #11E81 #16K20 #19D45 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:11E04 #msc:11E81 #msc:16K20 #msc:19D45

paper · pdf · doi:10.48550/arxiv.1901.00358

arxiv created 2019/11/04 · arxiv updated 2019/11/05

Abstract

Given a field F of characteristic 3 and division symbol p-algebras [α,β)_3,F and [α,γ)_3,F of degree 3 over F, we prove that if αdlog(β)\wedge dlog(γ) is trivial in the Kato-Milne cohomology group H₃³(F) then the algebras share a common splitting field which is an inseparable degree 3 extension of either F or a quadratic extension of F. In the special case of quadratically closed fields, if αdlog(β)\wedge dlog(γ)=0, then they share an inseparable degree 3 extension of F.

Related

• Common Splitting Fields of Symbol Algebras
• The Bloch--Kato conjecture, decomposing fields, and generating cohomology in degree one
• Essential Dimension of Generic Symbols in Characteristic p
• Linkage of Sets of Cyclic Algebras
• Some split symbol algebras of prime degree