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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Explicit class field theory for rational function fields

Author: D. R. Hayes
Journal: Trans. Amer. Math. Soc. 189 (1974), 77-91
MSC: Primary 12A65; Secondary 12A90
MathSciNet review: 0330106
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Abstract: Developing an idea of Carlitz, I show how one can describe explicitly the maximal abelian extension of the rational function field over ${{\mathbf {F}}_q}$ (the finite field of q elements) and the action of the idèle class group via the reciprocity law homomorphism. The theory is closely analogous to the classical theory of cyclotomic extensions of the rational numbers.

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Keywords: Rational function field over a finite field, explicit class field theory, cyclotomic extensions
Article copyright: © Copyright 1974 American Mathematical Society