Similitudes of Algebras with Involution Under Odd-Degree Extensions

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.