Deformations of dihedral -group extensions

of fields

Author:
Elena V. Black

Journal:
Trans. Amer. Math. Soc. **351** (1999), 3229-3241

MSC (1991):
Primary 11R32, 11R58, 14E20, 14D10; Secondary 12F12, 12F10, 13B05

DOI:
https://doi.org/10.1090/S0002-9947-99-02135-2

Published electronically:
February 10, 1999

MathSciNet review:
1467461

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a -Galois extension of number fields we ask whether it is a specialization of a regular -Galois cover of . This is the ``inverse" of the usual use of the Hilbert Irreducibility Theorem in the Inverse Galois problem. We show that for many groups such arithmetic liftings exist by observing that the existence of generic extensions implies the arithmetic lifting property. We explicitly construct generic extensions for dihedral -groups under certain assumptions on the base field . We also show that dihedral groups of order and have generic extensions over any base field with characteristic different from .

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Additional Information

**Elena V. Black**

Affiliation:
Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6395

Address at time of publication:
Department of Mathematics, University of Oklahoma, 601 Elm Avenue, Room 423, Norman, Oklahoma 73019

Email:
eblack@math.ou.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02135-2

Received by editor(s):
May 15, 1996

Received by editor(s) in revised form:
September 18, 1996, and April 18, 1997

Published electronically:
February 10, 1999

Article copyright:
© Copyright 1999
American Mathematical Society