On normal integral bases of unramified abelian p-extensions over a global function field of characteristic p
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TLDR
It is proved that for a finite abelian p-extension L/K, it has a relative normal integral basis (NIB) if and only if it is unramified outside S.About:
This article is published in Finite Fields and Their Applications.The article was published on 2004-07-01 and is currently open access. It has received 3 citations till now. The article focuses on the topics: Genus field & Algebraic function field.read more
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On the Galois module structure of extensions of local fields
TL;DR: A survey of the theory of Galois module structure for extensions of local fields can be found in this article, where the authors present a survey of recent progress on this subject and motivate an exposition of this theory.
Journal ArticleDOI
Analysis of the classical cyclotomic approach to Fermat's last Theorem
TL;DR: In this article, the cyclotomic approach to Fermat's last theorem using class field theory (essentially the reflection theorems), without any calculations, has been shown to be possible.
References
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Book
Graduate Texts in Mathematics
Rajendra Bhatia,Glen Bredon,Wolfgang Walter,Joseph J. Rotman,M. Ram Murty,Jane Gilman,Peter Walters,Martin Golubitsky,Ioannis Karatzas,Henri Cohen,Raoul Bott,Gaisi Takeuti,Béla Bollobás,John M. Lee,Jiří Matoušek,Saunders Mac Lane,John L. Kelley,B. A. Dubrovin,Tom M. Apostol,John Stillwell,William Arveson +20 more
Book
Number Theory in Function Fields
TL;DR: In this article, the behavior of the class group in constant field extensions is investigated and the Brumer-Stark Conjecture is shown to hold for S-Units, S-Class Group, and Corresponding L-functions.
MonographDOI
Algebraic Number Theory
A. Fröhlich,Martin J. Taylor +1 more
TL;DR: In this article, Algebraic foundations and Dedekind domains have been used to define classes and units of low degree fields of cyclotomic fields and Diophantine equations.
Journal ArticleDOI
Explicit class field theory for rational function fields
TL;DR: In this article, it was shown how one can describe explicitly the maximal abelian extension of the rational function field over F, (the finite field of q elements) and the action of the idèle class group via reciprocity law homomorphism.
Book
Cyclic Galois Extensions of Commutative Rings
TL;DR: Galois theory of commutative rings and cyclic Galois theory without the condition "p?1? R". as mentioned in this paper, where R is the number of cyclic p-extensions.