代数数论
作者：(德)诺伊基希(Jürgen,N.)著
出版：科学出版社有限责任公司 2016.4
丛书：国外数学名著系列（影印版）
版本：31
定价：198.00 元
ISBN-13：9787030182890
ISBN-10：7030182898 去豆瓣看看
出版：科学出版社有限责任公司 2016.4
丛书：国外数学名著系列（影印版）
版本：31
定价：198.00 元
ISBN-13：9787030182890
ISBN-10：7030182898 去豆瓣看看
目 录内容简介
Chapter Ⅰ：Algebraic Integers
1. The Gaussian Integers
2. Integrality
3. Ideals
4. Lattices
5. Minkowski Theory
6. The Class Number
7. Dirichlet's Unit Theorem
8. Extensions of Dedekind Domains
9. Hilbert's Ramification Theory
查看完整
1. The Gaussian Integers
2. Integrality
3. Ideals
4. Lattices
5. Minkowski Theory
6. The Class Number
7. Dirichlet's Unit Theorem
8. Extensions of Dedekind Domains
9. Hilbert's Ramification Theory
查看完整
目 录内容简介
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目 录内容简介
Chapter Ⅰ：Algebraic Integers
1. The Gaussian Integers
2. Integrality
3. Ideals
4. Lattices
5. Minkowski Theory
6. The Class Number
7. Dirichlet's Unit Theorem
8. Extensions of Dedekind Domains
9. Hilbert's Ramification Theory
10. Cyclotomic Fields
11. Localization
12. Orders
13. One-dimensional Schemes
14. Function Fields
Chapter Ⅱ：The Theory of Valuations
1. The p-adic Numbers
2. The p-adic Absolute Value
3. Valuations
4. Completions
5. Local Fields
6. Henselian Fields
7. Unramified and Tamely Ramified Extensions
8. Extensions of Valuations
9. Galois Theory of Valuations
10. Higher Ramification Groups
Chapter Ⅲ：Riemann-Roeh Theory
1. Primes
2. Different and Discriminant
3. Riemann-Roch
4. Metrized o-Modules
5. Grothendieck Groups
6. The Chern Character
7. Grothendieck-Riemann-Roch
8. The Euler-Minkow.ski Characteristic
Chapter Ⅳ：Abstract Class Field Theory
1. Infinite Galois Theory
2. Projective and Inductive Limits
3. Abstract Galois Theory
4. Abstract Valuation Theory
5. The Reciprocity Map
6. The General Reciprocity Law
7. The Herbrand Quotient
Chapter Ⅴ：Local Class Field Theory
1. The Local Reciprocity Law
2. The Norm Residue Symbol over Q(p)
3. The Hilbert Symbol
4. Formal Groups
5. Generalized Cyclotomic Theory
6. Higher Ramification Groups
Chapter Ⅵ：Global Class Field Theory
1. Idèles and Idèle Classes
2. Idèles in Field Extensions
3. The Herbrand Quotient of the Idèle Class Group
4. The Class Field Axiom
5. The Global Reciprocity Law
6. Global Class Fields
7. The Ideal-Theoretic Version of Class Field Theory
8. The Reciprocity Law of the Power Residues
Chapter Ⅶ：Zeta Functions and L-series
1. The Riemann Zeta Function
2. Dirichlet L-series
3. Theta Series
4. The Higher-dimensional Gamma Function
5. The Dedekind Zeta Function
6. Hecke Characters
7. Theta Series of Algebraic Number Fields
8. Hecke L-series
9. Values of Dirichlet L-series at Integer Points
10. Artin L-series
11. The Artin Conductor
12. The Functional Equation of Artin L-series
13. Density Theorems
Bibliography
Index
^ 收 起
1. The Gaussian Integers
2. Integrality
3. Ideals
4. Lattices
5. Minkowski Theory
6. The Class Number
7. Dirichlet's Unit Theorem
8. Extensions of Dedekind Domains
9. Hilbert's Ramification Theory
10. Cyclotomic Fields
11. Localization
12. Orders
13. One-dimensional Schemes
14. Function Fields
Chapter Ⅱ：The Theory of Valuations
1. The p-adic Numbers
2. The p-adic Absolute Value
3. Valuations
4. Completions
5. Local Fields
6. Henselian Fields
7. Unramified and Tamely Ramified Extensions
8. Extensions of Valuations
9. Galois Theory of Valuations
10. Higher Ramification Groups
Chapter Ⅲ：Riemann-Roeh Theory
1. Primes
2. Different and Discriminant
3. Riemann-Roch
4. Metrized o-Modules
5. Grothendieck Groups
6. The Chern Character
7. Grothendieck-Riemann-Roch
8. The Euler-Minkow.ski Characteristic
Chapter Ⅳ：Abstract Class Field Theory
1. Infinite Galois Theory
2. Projective and Inductive Limits
3. Abstract Galois Theory
4. Abstract Valuation Theory
5. The Reciprocity Map
6. The General Reciprocity Law
7. The Herbrand Quotient
Chapter Ⅴ：Local Class Field Theory
1. The Local Reciprocity Law
2. The Norm Residue Symbol over Q(p)
3. The Hilbert Symbol
4. Formal Groups
5. Generalized Cyclotomic Theory
6. Higher Ramification Groups
Chapter Ⅵ：Global Class Field Theory
1. Idèles and Idèle Classes
2. Idèles in Field Extensions
3. The Herbrand Quotient of the Idèle Class Group
4. The Class Field Axiom
5. The Global Reciprocity Law
6. Global Class Fields
7. The Ideal-Theoretic Version of Class Field Theory
8. The Reciprocity Law of the Power Residues
Chapter Ⅶ：Zeta Functions and L-series
1. The Riemann Zeta Function
2. Dirichlet L-series
3. Theta Series
4. The Higher-dimensional Gamma Function
5. The Dedekind Zeta Function
6. Hecke Characters
7. Theta Series of Algebraic Number Fields
8. Hecke L-series
9. Values of Dirichlet L-series at Integer Points
10. Artin L-series
11. The Artin Conductor
12. The Functional Equation of Artin L-series
13. Density Theorems
Bibliography
Index
^ 收 起
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