2018/06/10 by Chapman, Adam, Dolphin, Andrew
#11E04 #11E81 (primary) #16K20 #19D45 (secondary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1806.03603
Given a field F of positive characteristic p, θ∈ Hpn-1(F) and β,γ∈ F^×, we prove that if the symbols θ\wedge \fracd ββ and θ\wedge \fracd γγ in Hpn(F) share the same factors in Hp1(F) then the symbol θ\wedge \fracd ββ \wedge \fracd γγ in Hpn+1(F) is trivial. We conclude that when p=2, every two totally separably (n-1)-linked n-fold quadratic Pfister forms are inseparably (n-1)-linked. We also describe how to construct non-isomorphic n-fold Pfister forms which are totally separably (or inseparably) (n-1)-linked, i.e. share all common (n-1)-fold quadratic (or bilinear) Pfister factors.