| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910144598803321 |
|
|
Autore |
Adelmann Clemens |
|
|
Titolo |
The Decomposition of Primes in Torsion Point Fields / / by Clemens Adelmann |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2001 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Edizione |
[1st ed. 2001.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (VIII, 148 p.) |
|
|
|
|
|
|
Collana |
|
Lecture Notes in Mathematics, , 0075-8434 ; ; 1761 |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Number theory |
Algebraic geometry |
Number Theory |
Algebraic Geometry |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
Bibliographic Level Mode of Issuance: Monograph |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references and index. |
|
|
|
|
|
|
Nota di contenuto |
|
Introduction -- Decomposition laws -- Elliptic curves -- Elliptic modular curves -- Torsion point fields -- Invariants and resolvent polynomials -- Appendix: Invariants of elliptic modular curves; L-series coefficients a p; Fully decomposed prime numbers; Resolvent polynomials; Free resolution of the invariant algebra. |
|
|
|
|
|
|
|
|
Sommario/riassunto |
|
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. |
|
|
|
|
|
| |