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Autore: | Adelmann Clemens |
Titolo: | The Decomposition of Primes in Torsion Point Fields [[electronic resource] /] / by Clemens Adelmann |
Pubblicazione: | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2001 |
Edizione: | 1st ed. 2001. |
Descrizione fisica: | 1 online resource (VIII, 148 p.) |
Disciplina: | 512/.4 |
Soggetto topico: | Number theory |
Algebraic geometry | |
Number Theory | |
Algebraic Geometry | |
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. |
Titolo autorizzato: | Decomposition of primes in torsion point fields |
ISBN: | 3-540-44949-3 |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 996466380003316 |
Lo trovi qui: | Univ. di Salerno |
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