The graded Witt group kernel of biquadratic extensions in characteristic two

Baeza showed that when char(F)=2char(F)=2 if E/FE/F is the separable biquadratic extension E=F[℘−1(b1),℘−1(b2)]E=F[℘−1(b1),℘−1(b2)], thenker[Wq(F)→Wq(E)]=WF⋅[1,b1]+WF⋅[1,b2].ker[Wq(F)→Wq(E)]=WF⋅[1,b1]+WF⋅[1,b2]. Here we give the analogous result for the graded Witt group. Specifically we obtain an exact sequence νF(n,1)⊕νF(n,1)→H2n+1F→H2n+1E from which the result for GWqFGWqF follows by the isomorphisms of Kato. Applications to 2-algebras of exponent and index 4 are also given.