Introduction to Arakelov Theory

By: Serge Lang

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Hardcover | 23 November 1988

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204 Pages

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23.39 x 15.6 x 1.27

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Arakelov introduced a component at infinity in arithmetic considerations, thus giving rise to global theorems similar to those of the theory of surfaces, but in an arithmetic context over the ring of integers of a number field. The book gives an introduction to this theory, including the analogues of the Hodge Index Theorem, the Arakelov adjunction formula, and the Faltings Riemann-Roch theorem. The book is intended for second year graduate students and researchers in the field who want a systematic introduction to the subject. The residue theorem, which forms the basis for the adjunction formula, is proved by a direct method due to Kunz and Waldi. The Faltings Riemann-Roch theorem is proved without assumptions of semistability. An effort has been made to include all necessary details, and as complete references as possible, especially to needed facts of analysis for Green's functions and the Faltings metrics.

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You Can Find This Book In

Non-Fiction Mathematics Geometry Algebraic Geometry Number Theory Algebra

Foreword
Metrics and Chern Forms
Green's Functions on Riemann Surfaces
Intersections on an Arithmetic Surface
Hodge Index Theorem and the Adjunction Formula
The Faltings Riemann-Roch Theorem
Faltings Volumes on Cohomology
Diophantine Inequalities and Arakelov Theory
References
Freqently Used Symbols
Index
Table of Contents provided by Publisher. All Rights Reserved.

Introduction to Arakelov Theory

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Hardcover

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