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Diophantine Approximation and Abelian Varieties

The 13 chapters of this book centre around the proof of Theorem 1 of Faltings' paper Diophantine approximation on abelian;

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Number Theory and Algebraic Geometry

Abelian and Fano varieties.;

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Metric Diophantine Approximation on Manifolds

This 1999 book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a;

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Logarithmic Forms and Diophantine Geometry

, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries;

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Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation

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O Minimality & Diophantine Geometry

and model theoretic aspects of the subject. These include Martin Orr's survey of abelian varieties, Christopher Daw's introduction to Shimura;

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Arithmetic Compactifications of PEL-Type Shimura Varieties

accessible to graduate students who have an understanding of schemes and abelian varieties. PEL-type Shimura varieties, which are natural;

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Applications of Diophantine Approximation to Integral Points and Transcendence

This introduction to the theory of Diophantine approximation pays special regard to Schmidt's subspace theorem and to its applications to;

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Complex Multiplication and Lifting Problems

Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary;

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Abelian Varieties

on Tate's theorem on endomorphisms of abelian varieties over finite fields (by C. P. Ramanujam) and on the Mordell - Weil theorem (by Yuri;

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The Gross-Zagier Formula on Shimura Curves

abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and;

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The Gross-Zagier Formula on Shimura Curves

abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and;

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Diophantine Approximation and Dirichlet Series

characterization by Gordon and Hedenmalm. The book is devoted to Diophantine approximation, the analytic theory of Dirichlet series and their composition;

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Diophantine Approximation and Dirichlet Series

characterization by Gordon and Hedenmalm. The book is devoted to Diophantine approximation, the analytic theory of Dirichlet series and their composition;

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Complex Tori and Abelian Varieties

This graduate-level textbook introduces the classical theory of complex tori and abelian varieties, while presenting in parallel more;

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Diophantine Approximation and Dirichlet Series

of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the;

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Compactifying Moduli Spaces for Abelian Varieties

The problem of compactifying the moduli spaceA of principally polarized g abelian varieties has a long and rich history. The majority;

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Discriminant Equations In Diophantine Nu

approximation and Diophantine geometry. This book is the first comprehensive account of discriminant equations and their applications. It brings;

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London Mathematical Society Lecture Note Series

workers in transcendence theory, Diophantine approximation and exponential sums.;

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Distribution Theory of Algebraic Numbers

The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals;

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Geometry of Moduli

in algebraic geometry, and this is reflected in the list of moduli spaces addressed in this volume: sheaves on varieties, symmetric tensors, abelian;

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Integral Points on Algebraic Varieties

points on algebraic varieties. This text rapidly introduces problems in Diophantine Geometry, especially those involving integral points;

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London Mathematical Society Lecture Note Series

theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this;

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Distribution Modulo One And Diophantine Approximation

This book presents state-of-the-art research on the distribution modulo one of sequences of integral powers of real numbers and related;

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Lecture Notes on Diophantine Analysis

general problems. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's;

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Recent Progress in Multivariate Approximation

-Bommerholz, September 24-29, 2000. Nineteen selected, peer-reviewed contributions cover recent topics in constructive approximation on varieties;

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Abelian Varieties with Complex Multiplication and Modular Functions

laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. This;

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