000 02284nam a2200325Ia 4500
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020 _a9783642824678 (pbk.)
_c€ 79.99
040 _bENG
_cIISER-BPR
041 _aENG
082 _a512.32
_bNEU
_223rd
100 _aNeukirch, Jurgen
_91066
222 _aMathematics
245 0 _aClass field theory
250 _a1st ed.
260 _aBerlin:
_bSpringer-Verlag,
_cc1986.
300 _aviii, 140p. :
_c24cm
440 _aA series of comprehensive studies in mathematics
_vVol. 280
_92565
504 _aIncludes literature and subject index.
520 _aClass field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by comparison with the results, rather imper­ spicuous system of arguments which have tended to jump around all over the place. My earlier presentation of the theory [41] has strengthened me in the belief that a highly elaborate mechanism, such as, for example, cohomol­ ogy, might not be adequate for a number-theoretical law admitting a very direct formulation, and that the truth of such a law must be susceptible to a far more immediate insight. I was determined to write the present, new account of class field theory by the discovery that, in fact, both the local and the global reciprocity laws may be subsumed under a purely group­ theoretical principle, admitting an entirely elementary description. This de­ scription makes possible a new foundation for the entire theory. The rapid advance to the main theorems of class field theory which results from this approach has made it possible to include in this volume the most important consequences and elaborations, and further related theories, with the excep­ tion of the cohomology version which I have this time excluded. This remains a significant variant, rich in application, but its principal results should be directly obtained from the material treated here.
650 _aMathematics
_92566
650 _aAlgebra
_92567
650 _aFields
_92568
650 _aGalois fields
_92569
942 _cBK
_2ddc
942 _2ddc
947 _a7331.0835
948 _a22
999 _c4206
_d4206