- Page 1: A Brief Introduction to Classical a
- Page 4 and 5: 4 CONTENTS 8 Factoring Primes 49 8.
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- Page 10 and 11: 10 CHAPTER 2. INTRODUCTION 2.2 What
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- Page 15 and 16: Chapter 3 Finitely generated abelia
- Page 17 and 18: 1. By permuting rows and columns, m
- Page 19 and 20: Chapter 4 Commutative Algebra We wi
- Page 21 and 22: 4.1. NOETHERIAN RINGS AND MODULES 2
- Page 23 and 24: 4.1. NOETHERIAN RINGS AND MODULES 2
- Page 25 and 26: Chapter 5 Rings of Algebraic Intege
- Page 27 and 28: 5.2. NORMS AND TRACES 27 because Z
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- Page 31 and 32: Chapter 6 Unique Factorization of I
- Page 33 and 34: 6.1. DEDEKIND DOMAINS 33 of a gener
- Page 35 and 36: 6.1. DEDEKIND DOMAINS 35 Theorem 6.
- Page 37 and 38: Chapter 7 Computing 7.1 Algorithms
- Page 39 and 40: 7.2. USING MAGMA 39 > S, P, Q := Sm
- Page 41 and 42: 7.2. USING MAGMA 41 r4 + r1 > Minim
- Page 43 and 44: 7.2. USING MAGMA 43 [ 1, a, 1/3*(a^
- Page 45 and 46: 7.2. USING MAGMA 45 7.2.4 Ideals >
- Page 47 and 48: 7.2. USING MAGMA 47 > OK := Maximal
- Page 49 and 50: Chapter 8 Factoring Primes First we
- Page 51 and 52: 8.1. FACTORING PRIMES 51 [3, 1, 0,
- Page 53 and 54: 8.1. FACTORING PRIMES 53 Theorem 8.
- Page 55 and 56: 8.1. FACTORING PRIMES 55 Sketch of
- Page 57 and 58: Chapter 9 Chinese Remainder Theorem
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9.1. THE CHINESE REMAINDER THEOREM
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9.1. THE CHINESE REMAINDER THEOREM
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Chapter 10 Discrimannts, Norms, and
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10.2. DISCRIMINANTS 65 Lemma 10.2.1
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10.4. FINITENESS OF THE CLASS GROUP
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10.4. FINITENESS OF THE CLASS GROUP
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10.4. FINITENESS OF THE CLASS GROUP
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Chapter 11 Computing Class Groups I
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11.1. REMARKS ON COMPUTING THE CLAS
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Chapter 12 Dirichlet’s Unit Theor
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12.1. THE GROUP OF UNITS 79 Lemma 1
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12.2. FINISHING THE PROOF OF DIRICH
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12.2. FINISHING THE PROOF OF DIRICH
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12.3. SOME EXAMPLES OF UNITS IN NUM
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12.3. SOME EXAMPLES OF UNITS IN NUM
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12.4. PREVIEW 89 > time G,phi := Un
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Chapter 13 Decomposition and Inerti
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13.2. DECOMPOSITION OF PRIMES 93 If
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13.2. DECOMPOSITION OF PRIMES 95 Th
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Chapter 14 Decomposition Groups and
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14.1. THE DECOMPOSITION GROUP 99 Th
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14.2. FROBENIUS ELEMENTS 101 Figure
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14.3. GALOIS REPRESENTATIONS AND A
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Part II Adelic Viewpoint 105
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108 CHAPTER 15. VALUATIONS Note tha
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110 CHAPTER 15. VALUATIONS To say t
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112 CHAPTER 15. VALUATIONS Proof. F
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114 CHAPTER 15. VALUATIONS 1 so |u|
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116 CHAPTER 15. VALUATIONS of a val
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118 CHAPTER 16. TOPOLOGY AND COMPLE
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120 CHAPTER 16. TOPOLOGY AND COMPLE
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122 CHAPTER 16. TOPOLOGY AND COMPLE
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124 CHAPTER 16. TOPOLOGY AND COMPLE
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126 CHAPTER 16. TOPOLOGY AND COMPLE
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128 CHAPTER 16. TOPOLOGY AND COMPLE
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130 CHAPTER 17. ADIC NUMBERS: THE F
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132 CHAPTER 17. ADIC NUMBERS: THE F
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134 CHAPTER 17. ADIC NUMBERS: THE F
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136 CHAPTER 17. ADIC NUMBERS: THE F
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138 CHAPTER 18. NORMED SPACES AND T
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140 CHAPTER 18. NORMED SPACES AND T
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142 CHAPTER 18. NORMED SPACES AND T
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144 CHAPTER 18. NORMED SPACES AND T
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146CHAPTER 19. EXTENSIONS AND NORMA
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148CHAPTER 19. EXTENSIONS AND NORMA
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150CHAPTER 19. EXTENSIONS AND NORMA
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152CHAPTER 19. EXTENSIONS AND NORMA
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154 CHAPTER 20. GLOBAL FIELDS AND A
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156 CHAPTER 20. GLOBAL FIELDS AND A
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158 CHAPTER 20. GLOBAL FIELDS AND A
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160 CHAPTER 20. GLOBAL FIELDS AND A
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162 CHAPTER 20. GLOBAL FIELDS AND A
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164 CHAPTER 20. GLOBAL FIELDS AND A
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166 CHAPTER 20. GLOBAL FIELDS AND A
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168 CHAPTER 21. IDELES AND IDEALS E
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170 CHAPTER 21. IDELES AND IDEALS T
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172 CHAPTER 21. IDELES AND IDEALS P
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174 CHAPTER 22. EXERCISES 6. Find t
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176 CHAPTER 22. EXERCISES 22. (*) S
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178 CHAPTER 22. EXERCISES (a) The p
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180 CHAPTER 22. EXERCISES 60. Find
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182 CHAPTER 22. EXERCISES
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184 BIBLIOGRAPHY [Fre94] G. Frey (e
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186 INDEX complex n-dimensional rep
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188 INDEX lies over, 73 local compa
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190 INDEX valuations such that |a|