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Arakelov Geometry and Diophantine Applications

varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry;

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Lectures on Arakelov Geometry

in their proofs of outstanding conjectures in diophantine geometry. This account presents the work of Gillet and Soule, extending Arakelov geometry;

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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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Diophantine Geometry

This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which;

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Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves

, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over arithmetic curves. It contains a complete;

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Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves

, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over arithmetic curves. It contains a complete;

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Arithmetic and Geometry

The 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on;

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Mathematical Sciences Research Institute Publications

Model theory has made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. These applications;

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Mathematical Sciences Research Institute Publications

Model theory has made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. These applications;

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Heights in Diophantine Geometry

Diophantine geometry has been studied by number theorists for thousands of years, since the time of Pythagoras, and has continued to be a;

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Logarithmic Forms and Diophantine Geometry

There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed;

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Number Theory and Geometry

Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians;

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Diophantine Approximation and Abelian Varieties

varieties , Ann. Math.133 (1991) and together give an approach to the proof that is accessible to Ph.D-level students in number theory and;

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Diophantine Analysis

While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number;

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Diophantine Analysis

While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number;

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Integral Points on Algebraic Varieties

This book is intended to be an introduction to Diophantine Geometry. The central theme is the investigation of the distribution of integral;

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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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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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Exponential Diophantine Equations

This is a integrated presentation of the theory of exponential diophantine equations. The authors present, in a clear and unified fashion;

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Profinite Groups, Arithmetic, and Geometry. (AM-67), Volume 67

geometry and higher arithmetic is based, and to do so in a manner that emphasizes the many interesting lines of inquiry leading from these;

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Moduli Spaces and Arithmetic Geometry (Kyoto, 2004)

of those moduli papers. Arakelov geometry and rigid geometry are studied in arithmetic papers. In the two exceptions, integral Hodge classes on;

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Analytic Number Theory

, using results from algebraic geometry and the geometry of numbers; the theory of Siegel's zeros and of exceptional characters of L-functions;

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The Brauer-Grothendieck Group

applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and;

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Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127

The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The;

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The Gross-Zagier Formula on Shimura Curves

generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local;

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The Gross-Zagier Formula on Shimura Curves

generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local;

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Diophantine Approximation and Dirichlet Series

of the Hardy-Dirichlet space, and much more. Proofs throughout the book mix Hilbertian geometry, complex and harmonic analysis, number theory;

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