The Decomposition of Primes in Torsion Point Fields
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 behaviou...
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| Format: | Livre numérique |
| Langue: | Anglais |
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Berlin [etc.] :
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[20..].
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| Collection: | Lecture notes in mathematics
1761 |
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| Edition sous un autre format: | • The decomposition of primes in torsion point fields, Clemens Adelmann, 2001, Berlin, Springer, 1 vol. (VI-142 p.), Lecture notes in mathematics, 3-540-42035-5 • The Decomposition of Primes in Torsion Point Fields, Texte imprimé, 9783662185209 |
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| 041 | 0 | |a eng | |
| 082 | |a 510 | ||
| 100 | 1 | |a Adelmann, Clemens, |d 1965-...., |c mathématicien. | |
| 245 | 1 | 0 | |a The Decomposition of Primes in Torsion Point Fields |c Clemens Adelmann. |
| 260 | |a Berlin [etc.] : |b Springer. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Lecture notes in mathematics |v 1761 |x 1617-9692 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |a 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. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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. | ||
| 650 | |a Idéaux (algèbre) | ||
| 650 | |a Théorie de la torsion (algèbre) | ||
| 650 | |a Décomposition (mathématiques) | ||
| 776 | 0 | |0 071451536 |t The decomposition of primes in torsion point fields |f Clemens Adelmann |d 2001 |c Berlin |n Springer |p 1 vol. (VI-142 p.) |s Lecture notes in mathematics |z 3-540-42035-5 | |
| 776 | 0 | |t The Decomposition of Primes in Torsion Point Fields |b Texte imprimé |z 9783662185209 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/b80624 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-4P4BGJM8-P |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:750632887 |u https://ezproxy.univ-orleans.fr/login?url=https://doi.org/10.1007/b80624 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:753989301 |u https://ezproxy.insa-cvl.fr/login?qurl=https://doi.org/10.1007/b80624 |z Accès INSA CVL | |
| 997 | |0 972794 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||