Explicit class field theory for rational function fields
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- by D. R. Hayes PDF
- Trans. Amer. Math. Soc. 189 (1974), 77-91 Request permission
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.References
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E. Artin and J. Tate, Class field theory, Notes Distributed by the Department of Mathematics, Harvard University, Cambridge, Mass.
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- Leonard Carlitz, On certain functions connected with polynomials in a Galois field, Duke Math. J. 1 (1935), no. 2, 137–168. MR 1545872, DOI 10.1215/S0012-7094-35-00114-4
- J. W. S. Cassels and A. Fröhlich (eds.), Algebraic number theory, Academic Press, London; Thompson Book Co., Inc., Washington, D.C., 1967. MR 0215665
- Jonathan Lubin and John Tate, Formal complex multiplication in local fields, Ann. of Math. (2) 81 (1965), 380–387. MR 172878, DOI 10.2307/1970622
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 189 (1974), 77-91
- MSC: Primary 12A65; Secondary 12A90
- DOI: https://doi.org/10.1090/S0002-9947-1974-0330106-6
- MathSciNet review: 0330106