Cyclotomic fields II. Front Cover. Serge Lang. Springer-Verlag, Cyclotomic Fields II · S. Lang Limited preview – QR code for Cyclotomic fields II. 57 CROWELL/Fox. Introduction to Knot. Theory. 58 KOBLITZ. p-adic Numbers, p- adic. Analysis, and Zeta-Functions. 2nd ed. 59 LANG. Cyclotomic Fields. In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive . New York: Springer-Verlag, doi/ , ISBN , MR · Serge Lang, Cyclotomic Fields I and II.
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Proof of Theorem 5 1. The cyclotomic fields played a crucial role in the development of modern algebra and number theory because of their relation with Fermat’s last theorem. Iwasawa viewed cyclotomic fields as ccylotomic analogues for number fields of the constant field extensions of algebraic geometry, and wrote a great sequence of papers investigating towers of cyclotomic fields, and more generally, Galois extensions of number fields whose Galois group is isomorphic to the cycltomic group of p-adic integers.
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Cyclotomic Fields I and II – Serge Lang – Google Books
I started studying algebraic cycootomic theory last summer by going through Marcus book. The Formal Leopoldt Transform.
Maybe I need to read some more on algebraic number theory, I do not know. You didn’t answer the question.
Kummer’s work on the congruences for the class numbers of cyclotomic fields was generalized in the twentieth century by Iwasawa in Iwasawa theory and by Kubota and Leopoldt in their theory of p-adic zeta functions. Measures and Power Series.
In the mid ‘s, the theory of cyclotomic fields was taken up again by Iwasawa and Leopoldt. Sign up or log in Sign up using Google. The Closure of the Cyclotomic Units.
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It also contains tons of exercises. Algebraic number theory Cyclotomic fields. Views Read Edit View history. Relations in the Ideal Classes.
Fileds and Power Series in the Composite Case. Sign up using Facebook. This article includes a list of referencesbut its sources remain unclear because it has insufficient inline citations. Cyclotomic Fields I and II.
Cyclotomic fields II – Serge Lang – Google Books
The Main Theorem for Divisible x and 0 unit. Twistings and Stickelberger Ideals. The degree of the extension.
Basic Lemma and Applications. In number theorya cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to Qthe field of rational numbers. However, the success of this general theory has tended to obscure special facts proved by Kummer about cyclotomic fields which lie Application of the Logarithm to the Local Symbol.
Projective Limit of the Unit Groups. However, the success of this general theory has tended to obscure special facts proved by Kummer about cyclotomic fields which lie deeper than the general theory. The Index of the First Stickelberger Ideal.
I would just start by looking at Marcus’ Number Fields for the basic algebraic number theory.