Buy this book
- About this book
-
It is an historical goal of algebraic number theory to relate all algebraic extensionsofanumber?eldinauniquewaytostructuresthatareexclusively described in terms of the base ?eld. Suitable structures are the prime ideals of the ring of integers of the considered number ?eld. By examining the behaviouroftheprimeidealswhenembeddedintheextension?eld,su?cient information should be collected to distinguish the given extension from all other possible extension ?elds. The ring of integers O of an algebraic number ?eld k is a Dedekind ring. k Any non-zero ideal in O possesses therefore a decomposition into a product k of prime ideals in O which is unique up to permutations of the factors. This k decomposition generalizes the prime factor decomposition of numbers in Z Z. In order to keep the uniqueness of the factors, view has to be changed from elements of O to ideals of O . k k Given an extension K/k of algebraic number ?elds and a prime ideal p of O , the decomposition law of K/k describes the product decomposition of k the ideal generated by p in O and names its characteristic quantities, i. e. K the number of di?erent prime ideal factors, their respective inertial degrees, and their respective rami?cation indices. Whenlookingatdecompositionlaws,weshouldinitiallyrestrictourselves to Galois extensions. This special case already o?ers quite a few di?culties.
- Table of contents (6 chapters)
-
-
Introduction
Pages 1-4
-
Decomposition Laws
Pages 5-24
-
Elliptic Curves
Pages 25-39
-
Elliptic Modular Curves
Pages 41-58
-
Torsion Point Fields
Pages 59-86
-
Table of contents (6 chapters)
Recommended for you
Bibliographic Information
- Bibliographic Information
-
- Book Title
- The Decomposition of Primes in Torsion Point Fields
- Authors
-
- Clemens Adelmann
- Series Title
- Lecture Notes in Mathematics
- Series Volume
- 1761
- Copyright
- 2001
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-540-44949-2
- DOI
- 10.1007/b80624
- Softcover ISBN
- 978-3-540-42035-4
- Series ISSN
- 0075-8434
- Edition Number
- 1
- Number of Pages
- VIII, 148
- Topics
*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works are not included.
