Logarithmic Forms and Diophantine Geometry

@inproceedings{Baker2008LogarithmicFA,
  title={Logarithmic Forms and Diophantine Geometry},
  author={Alan Baker and Gisbert W{\"u}stholz},
  year={2008}
}
Preface. 1. Transcendence origins 2. Logarithmic forms 3. Diophantine problems 4. Commutative algebraic groups 5. Multiplicity estimates 6. The analytic subgroup theorem 7. The quantitative theory 8. Further aspects of Diophantine geometry Bibliography Index. 
A Comprehensive Course in Number Theory
Preface Introduction 1. Divisibility 2. Arithmetical functions 3. Congruences 4. Quadratic residues 5. Quadratic forms 6. Diophantine approximation 7. Quadratic fields 8. Diophantine equations 9.
From Mordell to Zilber-Pink The Mordell conjecture
This lecture is concerned with some recent applications of mathematical logic to Diophantine geometry. More precisely it concerns applications of o-minimality, a branch of model theory which treats
Proofs of Transcendence Bachelor ’ s Project Mathematics
  • Mathematics
  • 2018
A transcendental number is a number which is not a root of a nonzero polynomial equation with integer or rational coefficients. This is a particularly interesting field of study as there are many
An approach to Pillai's problem with the Pell sequence and the powers of 3
. In this paper, we consider the Diophantine equation P n − 3 a = ν and find all ν having at least two representations. In the proof of the main theorem, we use a version of the Baker-Davenport
Integral points on moduli schemes of elliptic curves
We combine the method of Faltings (Arakelov, Paršin, Szpiro) with the Shimura–Taniyama conjecture to prove effective finiteness results for integral points on moduli schemes of elliptic curves. For
Algebraization, Transcendence, and D-Group Schemes
  • J. Bost
  • Mathematics
    Notre Dame J. Formal Log.
  • 2013
TLDR
The Grothendieck Period Conjecture for cycles of codimension 1 in abelian varieties over $\bar{\mathbb Q}}$ is derived from a classical transcendence theorem \`a la Schneider-Lang.
An effective result of André-Oort type II
Using transcendence theory we prove the Andre-Oort conjecture in case of the Shimura variety AC. It is well known that this result implies the Andre-Oort conjecture for a product of two arbitrary
Effectively computing integral points on the moduli of smooth quartic curves
We prove an effective version of the Shafarevich conjecture (as proven by Faltings) for smooth quartic curves. To do so, we establish an effective version of Scholl's finiteness result for smooth del
The p-adic analytic subgroup theorem and applications
We prove a p-adic analogue of W\"ustholz's analytic subgroup theorem. We apply this result to show that a curve embedded in its Jacobian intersects the p-adic closure of the Mordell-Weil group
An effective result of André-Oort type
Using transcendence theory we prove the André-Oort conjecture in case of the Shimura variety AC. It is well known that this result implies the André-Oort conjecture for a product of two arbitrary
...
...

References

SHOWING 1-8 OF 8 REFERENCES
Heights in Diophantine Geometry
I. Heights II. Weil heights III. Linear tori IV. Small points V. The unit equation VI. Roth's theorem VII. The subspace theorem VIII. Abelian varieties IX. Neron-Tate heights X. The Mordell-Weil
Free Ideal Rings and Localization in General Rings
Preface Note to the reader Terminology, notations and conventions used List of special notation 0. Preliminaries on modules 1. Principal ideal domains 2. Firs, semifirs and the weak algorithm 3.
Kazhdan’s Property (T)
Let G be a locally compact (second countable) group and π:G → U(ℋ) a unitary representation of G on the (separable) Hilbert space ℋ.Of course,ℋ may or may not contain non-trivial vectors invariant
Representation Theory of Finite Reductive Groups
Introduction Notations and conventions Part I. Representing Finite BN-Pairs: 1. Cuspidality in finite groups 2. Finite BN-pairs 3. Modular Hecke algebras for finite BN-pairs 4. Modular duality
An Introduction to Involutive Structures 7 A. Shlapentokh Hilbert's Tenth Problem
    Logarithmic Forms and Diophantine Geometry
      All the titles listed below can be obtained from good booksellers or from
        Michler Theory of Finite Simple Groups