دانلود کتاب The Dynamical Mordell–Lang Conjecture

فهرست مطالب :

Cover
Preface
Notation
Chapter 1. Introduction
1.1. Overview of the problem
1.2. Linear recurrence sequences
1.3. Polynomial-exponential Diophantine equations
1.4. Linear algebra
1.5. Arithmetic geometry
1.6. Plan of the book
Chapter 2. Background material
2.1. Algebraic geometry
2.2. Dynamics of endomorphisms
2.3. Valuations
2.4. Chebotarev Density Theorem
2.5. The Skolem-Mahler-Lech Theorem
2.6. Heights
Chapter 3. The Dynamical Mordell-Lang problem
3.1. The Dynamical Mordell-Lang Conjecture
3.2. The case of rational self-maps
3.3. Known cases of the Dynamical Mordell-Lang Conjecture
3.4. The Mordell-Lang conjecture
3.5. Denis-Mordell-Lang conjecture
3.6. A more general Dynamical Mordell-Lang problem
Chapter 4. A geometric Skolem-Mahler-Lech Theorem
4.1. Geometric reformulation
4.2. Automorphisms of affine varieties
4.3. Étale maps
4.4. Proof of the Dynamical Mordell-Lang Conjecture for étale maps
Chapter 5. Linear relations between points in polynomial orbits
5.1. The main results
5.2. Intersections of polynomial orbits
5.3. A special case
5.4. Proof of Theorem 5.3.0.2
5.5. The general case of Theorem 5.3.0.1
5.6. The method of specialization and the proof of Theorem 5.5.0.2
5.7. The case of Theorem 5.2.0.1 when the polynomials have different degrees
5.8. An alternative proof for the function field case
5.9. Possible extensions
5.10. The case of plane curves
5.11. A Dynamical Mordell-Lang type question for polarizable endomorphisms
Chapter 6. Parametrization of orbits
6.1. Rational maps
6.2. Analytic uniformization
6.3. Higher dimensional parametrizations
Chapter 7. The split case in the Dynamical Mordell-Lang Conjecture
7.1. The case of rational maps without periodic critical points
7.2. Extension to polynomials with complex coefficients
7.3. The case of “almost” post-critically finite rational maps
Chapter 8. Heuristics for avoiding ramification
8.1. A random model heuristic
8.2. Random models and cycle lengths
8.3. Random models and avoiding ramification
8.4. The case of split maps
Chapter 9. Higher dimensional results
9.1. The Herman-Yoccoz method for periodic attracting points
9.2. The Herman-Yoccoz method for periodic indifferent points
9.3. The case of semiabelian varieties
9.4. Preliminaries from linear algebra
9.5. Proofs for Theorems 9.2.0.1 and 9.3.0.1
Chapter 10. Additional results towards the Dynamical Mordell-Lang Conjecture
10.1. A