Split embedding problems over the open arithmetic disc

Arno Fehm, Elad Paran

Research output: Contribution to journalArticlepeer-review


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 OK{t}, where OKis the ring of integers of an arbitrary number field K.

Original languageEnglish
Pages (from-to)3535-3551
Number of pages17
JournalTransactions of the American Mathematical Society
Issue number7
StatePublished - 2014

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© 2014 American Mathematical Society.


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