The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.

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

History

Faltings, Gerd

Americas

Princeton University Press

Lectures on the Arithmetic Riemann-Roch Theorem (Annals of Mathematics Studies)

Science & Math

Mathematics

This book consists of the notes from the seminar Bonn/ Wuppertal 1983/ 84 on Arithmetic Geometry. It contains a proof for the Mordell conjecture and may be useful as an introduction to Arakelov's point of view in diophantine geometry. The third edition includes an appendix in which a detailed survey on the spectacular recent developments in arithmetic algebraic geometry is given. These beautiful new results have their roots in the material covered by this book.

Rational Points: Seminar Bonn/Wuppertal 1983/84 (Aspects of Mathematics)

Wüstholz, Gisbert

Vieweg+Teubner Verlag

Rational Points: Seminar Bonn/Wuppertal 1983/84 A Publication of the Max-Planck-Institut für Mathematik, Bonn (Stuttgarter Beitrage Zur Historischen Migrationsforschung) (German Edition)

I: Moduli Spaces.- II: Heights.- III: Some Facts from the Theory of Group Schemes (Fritz Grunewald).- IV: Tate'S Conjecture on the Endomorphisms of Abelian Varieties (Norbert Schappacher).- V: The Finiteness Theorems of Faltings.- VI: Complements.- VII: Intersection Theory on Arithmetic Surfaces.

Rational Points: Seminar Bonn/Wuppertal 1983/84 (Aspects of Mathematics, 2)

A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.

Degeneration of Abelian Varieties (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 22)

Chai, Ching-Li

Springer

A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.

Degeneration of Abelian Varieties (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)

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Books by Faltings, Gerd

See the best price to sell, buy, or rent books by Faltings, Gerd. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

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

Lectures on the Arithmetic Riemann-Roch Theorem (Annals of Mathematics Studies)

Rational Points: Seminar Bonn/Wuppertal 1983/84 (Aspects of Mathematics)

Rational Points: Seminar Bonn/Wuppertal 1983/84 A Publication of the Max-Planck-Institut für Mathematik, Bonn (Stuttgarter Beitrage Zur Historischen Migrationsforschung) (German Edition)

Rational Points: Seminar Bonn/Wuppertal 1983/84 (Aspects of Mathematics, 2)

Rational Points: Seminar Bonn/Wuppertal 1983/84 (Aspects of Mathematics)

Degeneration of Abelian Varieties (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 22)

Degeneration of Abelian Varieties (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)