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arXiv · 1208.1044

Split embedding problems over the open arithmetic disc

Arno Fehm·Elad Paran
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Abstract

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{t}, where O is the ring of integers of an arbitrary number field K.

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Arno Fehm, Elad Paran. 2012-08-05. Split embedding problems over the open arithmetic disc. https://arxiv.org/abs/1208.1044

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