Split embedding problems over the open arithmetic disc

Let ℤ{t} be the ring of arithmetic power series that converge on the complex open unit disc. A classical result of Harbater asserts that every finite group occurs as a Galois group over the quotient field of ℤ{t}. We strengthen this by showing that every finite split embedding problem over ℚ acquires a solution over this field. More generally, we solve all t-unramified finite split embedding problems over the quotient field of O_K{t}, where O_Kis the ring of integers of an arbitrary number field K.