Author(s): Go Yamashita (山下 剛)
Year: 2019
Language: English
Commentary: with bookmarks
Pages: 409
Contents
0. Introduction.
0.1. Un Fil d'Ariane.
0.2. Notation.
1. Reduction Steps via General Arithmetic Geometry.
1.1. Height Functions.
1.2. First Reduction.
1.3. Second Reduction : Log-volume Computations.
1.4. Third Reduction : Choice of Initial Θ-Data.
2. Preliminaries on Anabelian Geometry.
2.1. Some Basics on Galois Groups of Local Fields.
2.2. Arithmetic Quotients.
2.3. Slimness and Commensurable Terminality.
2.4. Characterisation of Cuspidal Decomposition Groups.
3. Mono-anabelian Reconstruction Algorithms.
3.1. Some Definitions.
3.2. Belyi and Elliptic Cuspidalisations : Hidden Endomorphisms.
3.2.1. Elliptic Cuspidalisation.
3.2.2. Belyi Cuspidalisation.
3.3. Uchida's Lemma.
3.4. Mono-anabelian Reconstruction of the Base Field and Function Field.
3.5. On the Philosophy of Mono-analyticity and Arithmetic Holomorphicity.
4. The Archimedean Theory : Formulated Without Reference to a Specific Model C.
4.1. Aut-Holomorphic Spaces.
4.2. Elliptic Cuspidalisation and Kummer Theory in the ArchimedeanTheory.
4.3. On the Philosophy of Etale-like and Frobenius-like Objects.
4.4. Mono-anabelian Reconstruction Algorithms in the Archimedean Theory.
5. Log-volumes and Log-shells.
5.1. Non-Archimedean Places.
5.2. Archimedean Places.
6. Preliminaries on Tempered Fundamental Groups.
6.1. Some Definitions.
6.2. Profinite Conjugates vs. Tempered Conjugates.
7. Etale Theta Functions : Three Fundamental Rigidities.
7.1. Theta-related Varieties.
7.2. The Etale Theta Function.
7.3. l-th Root of the Etale Theta Function.
7.4. Three Fundamental Rigidities of Mono-theta Environments.
7.5. Some Analogous Objects at Good Places.
8. Frobenioids.
8.1. Elementary Frobenioids and Model Frobenioids.
8.2. Examples.
8.3. From Tempered Frobenioids to Mono-theta Environments.
9. Preliminaries on the NF Counterpart of Theta Evaluation.
9.1. Pseudo-Monoids of κ-Coric Functions.
9.2. Cyclotomic Rigidity via κ-Coric Functions.
9.3. ⊠-Line Bundles and ⊞-Line Bundles.
10. Hodge Theatres.
10.1. Initial Θ-Data.
10.2. Model Objects.
10.3. Θ-Hodge Theatres and Prime-strips.
10.4. The Multiplicative Symmetry ⊠ : ΘNF-Hodge Theatres and NF-, Θ-Bridges
10.5. The Additive Symmetry ⊞ : Θ^((+,-)ell)-Hodge Theatres and Θ^(ell)-,Θ^(+,-) -Bridges.
10.6. Θ^((+,-)ell)NF-Hodge Theatres : An Arithmetic Analogue of the Upper Half Plane.
11. Hodge-Arakelov-theoretic Evaluation Maps.
11.1. Radial Environments.
11.2. Hodge-Arakelov-theoretic Evaluation and Gaussian Monoids at Bad Places.
11.3. Hodge-Arakelov-theoretic Evaluation and Gaussian Monoids at Good Places.
11.4. Hodge-Arakelov-theoretic Evaluation and Gaussian Monoids in the Global Case.
12. Log-links : An Arithmetic Analogue of Analytic Continuation.
12.1. Log-links and Log-theta-lattices.
12.2. Kummer Compatible Multiradial Theta Monoids.
13. Multiradial Representation Algorithms.
13.1. Local and Global Packets.
13.2. Log-Kummer Correspondences and Multiradial Representation Algorithm
Appendix A. Motivation of the Definition of the Θ-Link
A.1. The Classical de Rham Comparison Theorem.
A.2. p-adic Hodge-theoretic Comparison Theorem.
A.3. Hodge-Arakelov-theoretic Comparison Theorem.
A.4. Motivation of the Definition of the Θ-Link
Appendix B. Anabelian Geometry.
Appendix C. Miscellany.
C.1. On the Height Function.
C.2. Non-critical Belyi Maps.
C.3. k-Cores.
C.4. On the Prime Number Theorem.
C.5. On the Residual Finiteness of Free Groups.
C.6. Some Lists on Inter-universal Teichmuller Theory.
Index of Terminologies
Index of Symbols
References
