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Taming wild extensions : Hopf algebras and local Galois module theory / Lindsay N. Childs.
Math/Physics/Astronomy Library QA613.8 .C48 2000
Available
- Format:
- Book
- Author/Creator:
- Childs, Lindsay.
- Series:
- Mathematical surveys and monographs ; no. 80.
- Mathematical surveys and monographs, 0076-5376 ; v. 80
- Language:
- English
- Subjects (All):
- Hopf algebras.
- Galois modules (Algebra).
- Field extensions (Mathematics).
- Physical Description:
- viii, 215 pages ; 27 cm.
- Place of Publication:
- Providence, R.I. : American Mathematical Society, [2000]
- Contents:
- Chapter 1. Hopf algebras and Galois extensions 7
- 1 Basic definitions and notation 7
- 2 Hopf algebras and R-algebras 14
- 3 Integrals 25
- 4 Short exact sequences of Hopf algebras 28
- 5 Hopf orders 39
- Chapter 2. Hopf Galois structures on separable field extensions 47
- 6 Greither-Pareigis theory 47
- 7 Byott's translation 56
- 8 Byott's uniqueness theorem 61
- 9 Prime power cyclic Galois extensions 64
- 10 Non-abelian extensions 66
- 11 Pure extensions 70
- Chapter 3. Tame extensions and Noether's Theorem 73
- 12 Associated orders 73
- 13 Tame extensions 75
- 14 Galois extensions 79
- Chapter 4. Hopf algebras of rank p 85
- 15 Rank p Hopf orders over algebraically closed fields 85
- 16 Eigenspace decompositions 87
- Chapter 5. Larson orders 97
- 17 Group valuations 97
- 18 Orders from valuations 99
- 19 Lattice properties 102
- 20 Uniqueness results 106
- 21 One-parameter Larson orders 109
- Chapter 6. Cyclic extensions of degree p 113
- 22 Different and discriminant 113
- 23 Ramification groups 120
- 24 Cyclic extensions of degree p 121
- Chapter 7. Non-maximal orders 129
- 25 Hopf Galois orders in Kummer extensions of order p 129
- 26 Orders and associated orders 132
- Chapter 8. Ramification restrictions 135
- 27 Ramification numbers 135
- 28 Tameness 141
- 29 When does tame imply Galois 142
- 30 Ramification conditions 143
- Chapter 9. Hopf algebras of rank p[superscript 2] 149
- 31 Hopf orders in KC[subscript p superscript 2] 149
- Chapter 10. Cyclic Hopf Galois extensions of degree p[superscript 2] 161
- 32 Valuation rings of cyclic extensions of degree p[superscript 2] 161
- Chapter 11. Formal groups 171
- 33 Formal groups 171
- 34 Formal groups and Hopf algebras 175
- 35 Height 177
- 36 Lubin-Tate formal groups 179
- 37 Oort embedding 183
- 38 Polynomial formal groups 185
- Chapter 12. Principal homogeneous spaces and formal groups 191
- 39 Kummer extensions 191
- 40 Which is the correct Hopf Galois structure 201.
- Notes:
- Includes bibliographical references (pages 205-211) and index.
- ISBN:
- 0821821318
- OCLC:
- 43648660
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