Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 12A65, 12A90

Retrieve articles in all journals with MSC: 12A65, 12A90


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0330106-6
PII: S 0002-9947(1974)0330106-6
Keywords: Rational function field over a finite field, explicit class field theory, cyclotomic extensions
Article copyright: © Copyright 1974 American Mathematical Society