## Split embedding problems over the open arithmetic disc

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- by Arno Fehm and Elad Paran PDF
- Trans. Amer. Math. Soc.
**366**(2014), 3535-3551 Request permission

## Abstract:

Let $\mathbb {Z}\{t\}$ 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 $\mathbb {Z}\{t\}$. We strengthen this by showing that every finite split embedding problem over $\mathbb {Q}$ acquires a solution over this field. More generally, we solve all $t$-unramified finite split embedding problems over the quotient field of $\mathcal {O}_K\{t\}$, where $\mathcal {O}_K$ is the ring of integers of an arbitrary number field $K$.## References

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## Additional Information

**Arno Fehm**- Affiliation: Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germany
- MR Author ID: 887431
- ORCID: 0000-0002-2170-9110
**Elad Paran**- Affiliation: Department of Mathematics and Computer Science, Open University of Israel, 43107 Raanana, Israel
- Received by editor(s): August 29, 2011
- Received by editor(s) in revised form: August 2, 2012
- Published electronically: February 26, 2014
- Additional Notes: This research was supported by the DFG program “Initiation and Intensification of Bilateral Cooperation”
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**366**(2014), 3535-3551 - MSC (2010): Primary 12E30, 12F12, 13J05
- DOI: https://doi.org/10.1090/S0002-9947-2014-05931-X
- MathSciNet review: 3192606