Finite abelian descent VSA conjecture for all number fields

Let $k$ be a number field. A variety satisfies VSA for $(\fab,f,k)$ if the corresponding finite abelian descent obstruction has the stated property of the paper. Finite abelian descent VSA conjecture. For any number field $k$, the answer to the paper's VSA question is yes for $(\fab,f,k)$. This would extend the result known for imaginary quadratic and totally real number fields to all number fields.