TY - JOUR

T1 - Split embedding problems over the open arithmetic disc

AU - Fehm, Arno

AU - Paran, Elad

N1 - Publisher Copyright:
© 2014 American Mathematical Society.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84924785550&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-2014-05931-X

DO - 10.1090/S0002-9947-2014-05931-X

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AN - SCOPUS:84924785550

SN - 0002-9947

VL - 366

SP - 3535

EP - 3551

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 7

ER -