The graded Witt group kernel of biquadratic extensions in characteristic two

Baeza showed that when char(F) = 2 if E/F is the separable biquadratic extension E = F[p(-1)(b(1)), p(-1)(b(2))], then ker[W-q(F) -> W-q(E)] = W F . [1, b(1)] + W F . [1, b(2)]. Here we give the analogous result for the graded Witt group. Specifically we obtain an exact sequence nu(F)(n,1) circle plus nu(F)(n,1) -> H-2(n+1) F -> H-2(n+1) E from which the result for GW(q)F follows by the isomorphisms of Kato. Applications to 2-algebras of exponent and index 4 are also given. (C) 2012 Elsevier Inc. All rights reserved.