| Dewey Class |
512.7 |
| Titel |
The Decomposition of Primes in Torsion Point Fields ([EBook] /) / edited by Clemens Adelmann. |
| Added Personal Name |
Adelmann, Clemens editor. |
| Other name(s) |
SpringerLink (Online service) |
| Veröffentl |
Berlin, Heidelberg : : Springer Berlin Heidelberg, , 2001. |
| Physical Details |
VIII, 148 p. : online resource. |
| Reihe |
Lecture Notes in Mathematics 0075-8434 ; ; 1761 |
| ISBN |
9783540449492 |
| Summary Note |
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.: |
| Contents note |
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. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/b80624 |
| LINKS ZU 'VERWANDTEN WERKEN |
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Algebraic Geometry .
Mathematics .
Number Theory .
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