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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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DOI: https://doi.org/10.1090/S0002-9947-1974-0330106-6
Keywords: Rational function field over a finite field, explicit class field theory, cyclotomic extensions
Article copyright: © Copyright 1974 American Mathematical Society