Deformations of dihedral group extensions of fields
Author:
Elena V. Black
Journal:
Trans. Amer. Math. Soc. 351 (1999), 32293241
MSC (1991):
Primary 11R32, 11R58, 14E20, 14D10; Secondary 12F12, 12F10, 13B05
Published electronically:
February 10, 1999
MathSciNet review:
1467461
Fulltext PDF Free Access
Abstract 
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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 191046395
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:
http://dx.doi.org/10.1090/S0002994799021352
PII:
S 00029947(99)021352
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
