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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Galois groups and complex multiplication


Author: Michael Fried
Journal: Trans. Amer. Math. Soc. 235 (1978), 141-163
MSC: Primary 14H30; Secondary 14H25
MathSciNet review: 472917
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Abstract: The Schur problem for rational functions is linked to the theory of complex multiplication and thereby solved. These considerations are viewed as a special case of a general problem, prosaically labeled the extension of constants problem. The relation between this paper and a letter of J. Herbrand to E. Noether (published posthumously) is speculatively summarized in a conjecture that may be regarded as an arithmetic version of Riemann's existence theorem.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0472917-6
PII: S 0002-9947(1978)0472917-6
Article copyright: © Copyright 1978 American Mathematical Society