p-adic Hodge Theory
β Bhargav Bhatt (editor), Martin Olsson (editor)
π Library
π
2020
π Springer
π English, French
β¦ LIBER β¦
π
p-adic heights and p-adic Hodge theory
β Scribed by Denis Benois
- Publisher
- SociΓ©tΓ© MathΓ©matique de France
- Year
- 2020
- Tongue
- English
- Leaves
- 150
- Series
- Memoires de la SociΓ©tΓ© MathΓ©matique de France 167
- Category
- Library
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β¦ Table of Contents
Introduction
0.1. Selmer complexes
0.2. Selmer complexes and (,)-modules
0.3. p-adic height pairings
0.4. General remarks
0.5. p-adic L-functions
0.6. The organization of this paper
Acknowledgements
Chapter 1. Complexes and products
1.1. The complex T(A)
1.2. Products
Chapter 2. Cohomology of (, K)-modules
2.1. (,K)-modules
2.2. Relation to p-adic Hodge theory
2.3. Local Galois cohomology
2.4. The complex C,K(D)
2.5. The complex K(V)
2.6. Transpositions
2.7. The Bockstein map
2.8. Iwasawa cohomology
2.9. The group H1f(D)
Chapter 3. p-adic height pairings I: Selmer complexes
3.1. Selmer complexes
3.2. p-adic height pairings
Chapter 4. Splitting submodules
4.1. Splitting submodules
4.2. The canonical splitting
4.3. Filtration associated to a splitting submodule
4.4. Appendix. Some semilinear algebra
Chapter 5. p-adic height pairings II: universal norms
5.1. The pairing hV,Dnorm
5.2. Comparision with hselV,D
Chapter 6. p-adic height pairings III: splitting of local extensions
6.1. The pairing hsplV,D
6.2. Comparison with NekovΓ‘Ε's height pairing
6.3. Comparision with hnormV,D
Chapter 7. p-adic height pairings IV: extended Selmer groups
7.1. Extended Selmer groups
7.2. Comparision with hsplV,D
7.3. The pairing hnormV,D for extended Selmer groups
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