Projective Schur groups of iterated power series fields

The Brauer–Witt Theorem states that every Schur algebra over a field K is Brauer equivalent to a cyclotomic algebra. A central conjecture on the projective Schur group of a field is the analogue of this theorem, which asserts that every projective Schur algebra over a field K is Brauer equivalent to a radical algebra. The conjecture is so far known to be true in characteristic p and for local and global fields. The next natural class of fields to test is power series fields over local and global fields. In this paper we verify the conjecture for these fields and more generally for iterated power series fields over local and global fields.