《類域論（英文版）》將gauss、legendre和其他的二次和更高階的互反率巧妙結(jié)合，并將這些結(jié)果更加一般化，是學(xué)習(xí)類域理論的入門書籍。《類域論（英文版）》運(yùn)用傳統(tǒng)方法和原始技巧呈現(xiàn)書中的材料，思路清晰流暢，是這個(gè)領(lǐng)域的圖書很難企及的�！额愑蛘摚ㄓ⑽陌妫房梢宰鳛榇鷶�(shù)數(shù)論的研究生教程，尤其適合自學(xué)。書中有大量的練習(xí)貫穿始終，已經(jīng)被證明了是一本很成功的教材。
1. A Brief Review
1. Number Fields
2. Completions of Number Fields
3. Some General Questions Motivating Class Field Theory
2. Dirichlefs Theorem on Primes in Arithmetic Progressions
1. Characters of Finite Abelian Groups
2. Dirichlet Characters
3. Dirichlet Series
4. Dirichlet抯 Theorem on Primes in Arithmetic Progressions
5. Dirichlet Density
3. Ray Class Groups
1. The Approximation Theorem and Infinite Primes
2. Ray Class Groups and the Universal Norm Index Inequality
3. The Main Theorems of Class Field Theory
4. The Idelic Theory
1. Places of a Number Field
2. A Little Topology
3. The Group of Id^ies of a Number Field
4. Cohomology of Finite Cyclic Groups and the Herbrand Quotient
5. Cyclic Galois Action on Ideles
5. Artin Reciprocity
1. The Conductor of an Abelian Extension of Number Fields and the Artin Symbol
2. Artin Reciprocity
3. An Example: Quadratic Reciprocity
4. Some Preibmnary Results about the Artin Map on Local Fields
6. The Existence Theorem, Consequences and Applications
1. The Ordering Theorem and the Reduction Lemma
2. Kummer n-extensions and the Proof of the Existence Theorem
3. The Artin Map on Local Fields
4. The Hilbert Class Field
5. Arbitrary Finite Extensions of Number Fields
6. Infinite Extensions and an Alternate Proof of the Existence Theorem
7. An Example; Cyclotomic Fields
7. Local Class Field Theory
1. Some Preliminary Facts About Local Fields
2. A Fundamental Exact Sequence
3. Local Units Modulo Norms
4. One-Dimensional Formal Group Laws
5. The Formal Group Laws of Lubin and Tate
6. Lubin-Tate Extensions
7. The Local Artin Map
Bibliography
Index
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