000 | 03430nam a22004815i 4500 | ||
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001 | 978-3-540-44949-2 | ||
003 | DE-He213 | ||
005 | 20190213151646.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s2001 gw | s |||| 0|eng d | ||
020 |
_a9783540449492 _9978-3-540-44949-2 |
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024 | 7 |
_a10.1007/b80624 _2doi |
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050 | 4 | _aQA241-247.5 | |
072 | 7 |
_aPBH _2bicssc |
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072 | 7 |
_aMAT022000 _2bisacsh |
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072 | 7 |
_aPBH _2thema |
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082 | 0 | 4 |
_a512.7 _223 |
245 | 1 | 4 |
_aThe Decomposition of Primes in Torsion Point Fields _h[electronic resource] / _cedited by Clemens Adelmann. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2001. |
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300 |
_aVIII, 148 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1761 |
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505 | 0 | _aIntroduction -- 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. | |
520 | _aIt 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 | 0 | _aNumber theory. | |
650 | 0 | _aGeometry, algebraic. | |
650 | 1 | 4 |
_aNumber Theory. _0http://scigraph.springernature.com/things/product-market-codes/M25001 |
650 | 2 | 4 |
_aAlgebraic Geometry. _0http://scigraph.springernature.com/things/product-market-codes/M11019 |
700 | 1 |
_aAdelmann, Clemens. _eeditor. _4edt _4http://id.loc.gov/vocabulary/relators/edt |
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710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783662185209 |
776 | 0 | 8 |
_iPrinted edition: _z9783540420354 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1761 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/b80624 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
999 |
_c11441 _d11441 |