2012/08/05 by Arno Fehm, Fehm, Arno, Elad Paran +1
Computer Science · Mathematics · #12E30 (Primary) #12F12 #13J05 (Secondary) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.AC #math.NT #msc:12E30 #msc:12F12 #msc:13J05
paper · pdf · doi:10.48550/arxiv.1208.1044
23 pages
arxiv created 2012/08/05 · openalex publication_date 2012/08/05 · arxiv updated 2012/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Zt 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 Zt. 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 Ot, where O is the ring of integers of an arbitrary number field K.