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|a 9783540449492
|9 978-3-540-44949-2
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|a 10.1007/b80624
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|a Adelmann, Clemens.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a The Decomposition of Primes in Torsion Point Fields
|h [electronic resource] /
|c by Clemens Adelmann.
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|a 1st ed. 2001.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg :
|b Imprint: Springer,
|c 2001.
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|a VIII, 148 p.
|b online resource.
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|a text
|b txt
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1761
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|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.
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|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.
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|a Number theory.
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|a Algebraic geometry.
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|a Number Theory.
|0 http://scigraph.springernature.com/things/product-market-codes/M25001
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|a Algebraic Geometry.
|0 http://scigraph.springernature.com/things/product-market-codes/M11019
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783662185209
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|i Printed edition:
|z 9783540420354
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1761
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|u https://doi.org/10.1007/b80624
|z Full Text via HEAL-Link
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|a Mathematics and Statistics (Springer-11649)
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