Arithmetic Geometry

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9781461386575: Arithmetic Geometry
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This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these expository lectures, this volume contains a translation into English of Falt≠ ings' seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation.

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Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties over arbitrary rings, in particular over non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory.
A C.I.M.E. Summer School devoted to arithmetic geometry was held in Cetraro, Italy in September 2007, and presented some of the most interesting new developments in arithmetic geometry.
This book collects the lecture notes which were written up by the speakers. The main topics concern diophantine equations, local-global principles, diophantine approximation and its relations to Nevanlinna theory, and rationally connected varieties.
The book is divided into three parts, corresponding to the courses given by J-L Colliot-Thélène Peter Swinnerton Dyer and Paul Vojta.

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9780387963112: Arithmetic Geometry

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ISBN 10:  0387963111 ISBN 13:  9780387963112
Publisher: Springer, 1986
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Book Description Springer-Verlag New York Inc., United States, 2011. Paperback. Condition: New. Language: English. Brand new Book. This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these expository lectures, this volume contains a translation into English of Falt- ings' seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation. Softcover reprint of the original 1st ed. 1986. Seller Inventory # KNV9781461386575

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M. Artin (contributions), G. Cornell (editor), C.-L. Chai (contributions), J. H. Silverman (editor), C.-L. Chinburg (contributions), G. Faltings (contributions), B. H. Gross (contributions), F. O. McGuiness (contributions), J. S. Milne (contributions), M. Rosen (contributions), S. S. Shatz (contributions), J. H. Silverman (contributions), P. Vojta (contributions)
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Book Description Springer-Verlag New York Inc., United States, 2011. Paperback. Condition: New. Language: English. Brand new Book. This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these expository lectures, this volume contains a translation into English of Falt- ings' seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation. Softcover reprint of the original 1st ed. 1986. Seller Inventory # LIE9781461386575

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Book Description Springer-Verlag New York Inc., United States, 2011. Paperback. Condition: New. Language: English. Brand new Book. This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these expository lectures, this volume contains a translation into English of Falt- ings' seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation. Softcover reprint of the original 1st ed. 1986. Seller Inventory # KNV9781461386575

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Book Description Condition: New. Publisher/Verlag: Springer, Berlin | This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these expository lectures, this volume contains a translation into English of Falt ings' seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation. | I Some Historical Notes.-1. The Theorems of Mordell and Mordell-Weil.-2. Siegel's Theorem About Integral Points.-3. The Proof of the Mordell Conjecture for Function Fields, by Manin and Grauert.-4. The New Ideas of Parshin and Arakelov, Relating the Conjectures of Mordell and Shafarevich.-5. The Work of Szpiro, Extending This to Positive Characteristic.-6. The Theorem of Tate About Endomorphisms of Abelian Varieties over Finite Fields.-7. The Work of Zarhin.- Bibliographic Remarks.- II Finiteness Theorems for Abelian Varieties over Number Fields.-1. Introduction.-2. Semiabelian Varieties.-3. Heights.-4. Isogenies.-5. Endomorphisms.-6. Finiteness Theorems.- References.- Erratum.- III Group Schemes, Formal Groups, and p-Divisible Groups.-1. Introduction.-2. Group Schemes, Generalities.-3. Finite Group Schemes.-4. Commutative Finite Group Schemes.-5. Formal Groups.-6. p-Divisible Groups.-7. Applications of Groups of Type (p, p,., p) to p-Divisible Groups.- References.- IV Abelian Varieties over ?.-0. Introduction.-1. Complex Tori.-2. Isogenies of Complex Tori.-3. Abelian Varieties.-4. The Néron-Severi Group and the Picard Group.-5. Polarizations and Polarized Abelian Manifolds.-6. The Space of Principally Polarized Abelian Manifolds.- References.- V Abelian Varieties.-1. Definitions.-2. Rigidity.-3. Rational Maps into Abelian Varieties.-4. Review of the Cohomology of Schemes.-5. The Seesaw Principle.-6. The Theorems of the Cube and the Square.-7. Abelian Varieties Are Projective.-8. Isogenies.-9. The Dual Abelian Variety: Definition.-10. The Dual Abelian Variety: Construction.-11. The Dual Exact Sequence.-12. Endomorphisms.-13. Polarizations and the Cohomology of Invertible Sheaves.-14. A Finiteness Theorem.-15. The Étale Cohomology of an Abelian Variety.-16. Pairings.-17. The Rosati Involution.-18. Two More Finiteness Theorems.-19. The Zeta Function of an Abelian Variety.-20. Abelian Schemes.- References.- VI The Theory of Height Functions.- The Classical Theory of Heights.-1. Absolute Values.-2. Height on Projective Space.-3. Heights on Projective Varieties.-4. Heights on Abelian Varieties.-5. The Mordell-Weil Theorem.- Heights and Metrized Line Bundles.-6. Metrized Line Bundles on Spec (R).-7. Metrized Line Bundles on Varieties.-8. Distance Functions and Logarithmic Singularities.- References.- VII Jacobian Varieties.-1. Definitions.-2. The Canonical Maps from C to its Jacobian Variety.-3. The Symmetric Powers of a Curve.-4. The Construction of the Jacobian Variety.-5. The Canonical Maps from the Symmetric Powers of C to its Jacobian Variety.-6. The Jacobian Variety as Albanese Variety; Autoduality.-7. Weil's Construction of the Jacobian Variety.-8. Generalizations.-9. Obta. Seller Inventory # K9781461386575

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