ABSTRACT
Let F be a field and L/F be an odd-degree extension. Let (A1, σ1) and (A2, σ2) be two central simple algebras with involution. We investigate in what cases (including when char(F) = 2), we have that (A1, σ1) and (A2, σ2) are similar over L implies they are already similar over F. This will have applications to the solution of injectivity problems in nonabelian galois cohomology.
Notes
Communicated by B. Parshall.