Abelian Varieties and Number Theory.

Cover
Title page
Contents
Preface
Bibliography
Abelian varieties and finitely generated Galois groups
1. Introduction
2. Probabilistic methods
3. Diophantine geometry
4. Combinatorics
5. Arithmetic
6. Analytic number theory
Acknowledgment
References
Ranks of abelian varieties and the full Mordell-Lang conjecture in dimension one
1. Introduction
Notation
2. Isotrivial and special curves
3. Rössler's theorem on inseparable points on curves
4. The Mordell-Lang conjecture
5. Proof of Theorem 1.1
6. Corollaries and applications
Acknowledgments
References
The group of automorphisms of the Heisenberg curve
1. Introduction
2. The triangle group approach
3. Restriction and lifting of automorphisms in covers
4. The Fermat curve
5. Automorphism group of the Heisenberg curve
6. Modular automorphisms
7. The curve ₃
Acknowledgment
References
Tate-Shafarevich groups of constant elliptic curves and isogeny volcanoes
1. Introduction
2. Preliminaries
3. Calculation of the Selmer group
4. Calculation of \Sha
5. Concluding remarks
Acknowledgments
References
Endomorphisms of ordinary superelliptic Jacobians
1. Introduction
2. Definitions and statements
3. The plan of the proof
4. Endomorphism algebras of abelian varieties
5. Abelian schemes
6. Proof of Theorem 3.1
7. Proof of Theorem 3.2
8. Superelliptic Jacobians
Acknowledgments
References
An introduction to Deuring's theory of constant reductions
Introduction
1. The Gauss valuation
2. Regular reduction
3. The inertia theorem
4. Reduction of genus
5. Good reduction
6. Almost all reductions
References
Purely inseparable points on curves
1. Introduction
2. Semistable sheaves
3. Proof of Theorem 1.1
Acknowledgments.

References
Correspondences on curves in positive characteristic
1. Introduction
2. Étale morphisms to the affine line
3. The main results and their proofs
4. Possible/impossible generalizations
Acknowledgments
References
The inverse Galois problem over ℂ( )
1. Introduction
2. Rings of holomorphic functions
3. Patching of Galois groups
Acknowledgment
References
Explicit Hilbert's irreducibility theorem in function fields
1. Introduction
2. Set-up and preliminaries
3. Separable polynomials
4. Inseparable polynomials
Acknowledgments
References
A comparison between obstructions to local-global principles over semi-global fields
Introduction
1. Completions and henselizations of semi-global fields
2. Local points on -varieties
3. Local-global principles for rational points
References
The generic monodromy of Drinfeld modular varieties in special characteristic
1. Statement of the main result
2. Formal -modules, -divisible groups and deformations of Drinfeld modules
3. The result of Strauch
4. Proof of Theorem \autoref{Thm:Main}
5. An example
6. An application
Acknowledgements
References
Symmetric tensor products of octonion algebras
Introduction
1. The associative case
2. Octonion algebras
3. Algebras of symmetric tensors
4. Central idempotents
5. Central simple algebras
References
Representations of étale fundamental groups and specialization of algebraic cycles
1. Introduction
2. Representation-theoretic results
3. Specialization of representations of the étale fundamental group and injectivity of the restriction morphism on ¹
4. Motivic representations
5. Specialization of the ℓ-adic Abel-Jacobi filtration on Chow groups
6. Applications, examples
Acknowledgments
References
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