Basic Number TheoryThe first part of this volume is based on a course taught at Princeton University in 1961-62. The author came upon a long-forgotten manuscript, which contained a brief but essentially complete account of the main features of classfield theory, both local and global, the inclusion of which greatly enhanced this volume. The author has tried to draw conclusions from the developments of the last thirty years, whereby locally compact groups, measure and integration have been seen to play an increasingly important role in classical number theory. |
Contents
Locally compact fields | 1 |
Lattices and duality over local fields | 24 |
Places of Afields | 43 |
Copyright | |
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A-field absolutely convergent algebraic closure algebraic extension algebraic number-field apply assertion assume basis canonical morphism ček Chap character of G characteristic p>1 clearly commutative completes the proof contained corollary of prop corresponding cosets cyclic extension defined definition denote division algebra divisor End(V factor-set field finite degree finite dimension finite place finite set follows at once formula fractional ideal Frobenius automorphism function G₁ Galois extension Galois group given group G Haar measure hence homomorphism identify implies integer isomorphism k-lattice K-linear K₁ kernel Ksep left vector-space lemma locally compact mapping maximal compact subring module monic polynomial morphism obvious open subgroup polynomial prime element proposition proves quasicharacter R-module roots shows simple algebra subfield subgroup of G subring subset theorem trivial unramified v₁ vector-space of finite w₁ write