A Brief Introduction to Classical and Adelic Algebraic ... - William Stein

More documents

Recommendations

Info

190 INDEX valuations such that |a| > 1 lemma, 153 value set stays same corollary, 120 volume, 68 volume of rings of integers lemma, 69 weak approximation theorem, 125
Page 1:
A Brief Introduction to Classical a
Page 4 and 5:
4 CONTENTS 8 Factoring Primes 49 8.
Page 6 and 7:
6 CONTENTS
Page 8 and 9:
8 CHAPTER 1. PREFACE Acknowledgemen
Page 10 and 11:
10 CHAPTER 2. INTRODUCTION 2.2 What
Page 12 and 13:
12 CHAPTER 2. INTRODUCTION (e) Deep
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
Page 29 and 30:
5.2. NORMS AND TRACES 29 elements o
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
Page 59 and 60:
9.1. THE CHINESE REMAINDER THEOREM
Page 61 and 62:
9.1. THE CHINESE REMAINDER THEOREM
Page 63 and 64:
Chapter 10 Discrimannts, Norms, and
Page 65 and 66:
10.2. DISCRIMINANTS 65 Lemma 10.2.1
Page 67 and 68:
10.4. FINITENESS OF THE CLASS GROUP
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Chapter 11 Computing Class Groups I
Page 75 and 76:
11.1. REMARKS ON COMPUTING THE CLAS
Page 77 and 78:
Chapter 12 Dirichlet’s Unit Theor
Page 79 and 80:
12.1. THE GROUP OF UNITS 79 Lemma 1
Page 81 and 82:
12.2. FINISHING THE PROOF OF DIRICH
Page 83 and 84:
12.2. FINISHING THE PROOF OF DIRICH
Page 85 and 86:
12.3. SOME EXAMPLES OF UNITS IN NUM
Page 87 and 88:
12.3. SOME EXAMPLES OF UNITS IN NUM
Page 89 and 90:
12.4. PREVIEW 89 > time G,phi := Un
Page 91 and 92:
Chapter 13 Decomposition and Inerti
Page 93 and 94:
13.2. DECOMPOSITION OF PRIMES 93 If
Page 95 and 96:
13.2. DECOMPOSITION OF PRIMES 95 Th
Page 97 and 98:
Chapter 14 Decomposition Groups and
Page 99 and 100:
14.1. THE DECOMPOSITION GROUP 99 Th
Page 101 and 102:
14.2. FROBENIUS ELEMENTS 101 Figure
Page 103 and 104:
14.3. GALOIS REPRESENTATIONS AND A
Page 105:
Part II Adelic Viewpoint 105
Page 108 and 109:
108 CHAPTER 15. VALUATIONS Note tha
Page 110 and 111:
110 CHAPTER 15. VALUATIONS To say t
Page 112 and 113:
112 CHAPTER 15. VALUATIONS Proof. F
Page 114 and 115:
114 CHAPTER 15. VALUATIONS 1 so |u|
Page 116 and 117:
116 CHAPTER 15. VALUATIONS of a val
Page 118 and 119:
118 CHAPTER 16. TOPOLOGY AND COMPLE
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
130 CHAPTER 17. ADIC NUMBERS: THE F
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
138 CHAPTER 18. NORMED SPACES AND T
Page 140 and 141: 140 CHAPTER 18. NORMED SPACES AND T
Page 146 and 147: 146CHAPTER 19. EXTENSIONS AND NORMA
Page 154 and 155: 154 CHAPTER 20. GLOBAL FIELDS AND A
Page 168 and 169: 168 CHAPTER 21. IDELES AND IDEALS E
Page 170 and 171: 170 CHAPTER 21. IDELES AND IDEALS T
Page 172 and 173: 172 CHAPTER 21. IDELES AND IDEALS P
Page 174 and 175: 174 CHAPTER 22. EXERCISES 6. Find t
Page 176 and 177: 176 CHAPTER 22. EXERCISES 22. (*) S
Page 178 and 179: 178 CHAPTER 22. EXERCISES (a) The p
Page 180 and 181: 180 CHAPTER 22. EXERCISES 60. Find
Page 182 and 183: 182 CHAPTER 22. EXERCISES
Page 184 and 185: 184 BIBLIOGRAPHY [Fre94] G. Frey (e
Page 186 and 187: 186 INDEX complex n-dimensional rep
Page 188 and 189: 188 INDEX lies over, 73 local compa
show all

A Brief Introduction to Classical and Adelic Algebraic ... - William Stein

Create successful ePaper yourself

Delete template?

Save as template?