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  • Produktbild: Arithmetic Geometry
  • Produktbild: Arithmetic Geometry

Arithmetic Geometry

Fr. 181.00

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

08.11.2011

Herausgeber

G. Cornell + weitere

Verlag

Springer Us

Seitenzahl

353

Maße (L/B/H)

23.5/15.5/2.1 cm

Gewicht

562 g

Auflage

Softcover reprint of the original 1st ed. 1986

Sprache

Englisch

ISBN

978-1-4613-8657-5

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

08.11.2011

Herausgeber

Verlag

Springer Us

Seitenzahl

353

Maße (L/B/H)

23.5/15.5/2.1 cm

Gewicht

562 g

Auflage

Softcover reprint of the original 1st ed. 1986

Sprache

Englisch

ISBN

978-1-4613-8657-5

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Arithmetic Geometry
  • Produktbild: Arithmetic Geometry
  • 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. Obtaining Coverings of a Curve from its Jacobian; Application to Mordell’s Conjecture.-
    10. Abelian Varieties Are Quotients of Jacobian Varieties.-
    11. The Zeta Function of a Curve.-
    12. Torelli’s Theorem: Statement and Applications.-
    13. Torelli’s Theorem: The Proof.- Bibliographic Notes for Abelian Varieties and Jacobian Varieties.- References.- VIII Néron Models.-
    1. Properties of the Néron Model, and Examples.-
    2. Weil’s Construction: Proof.-
    3. Existence of the Néron Model: R Strictly Local.-
    4. Projective Embedding.-
    5. Appendix: Prime Divisors.- References.- IX Siegel Moduli Schemes and Their Compactifications over ?.-
    0. Notations and Conventions.-
    1. The Moduli Functors and Their Coarse Moduli Schemes.-
    2. Transcendental Uniformization of the Moduli Spaces.-
    3. The Satake Compactification.-
    4. Toroidal Compactification.-
    5. Modular Heights.- References.- X Heights and Elliptic Curves.-
    1. The Height of an Elliptic Curve.-
    2. An Estimate for the Height.-
    3. Weil Curves.-
    4. A Relation with the Canonical Height.- References.- XI Lipman’s Proof of Resolution of Singularities for Surfaces.-
    1. Introduction.-
    2. Proper Intersection Numbers and the Vanishing Theorem.-
    3. Step 1: Reduction to Rational Singularities.-
    4. Basic Properties of Rational Singularities.-
    5. Step 2: Blowing Up the Dualizing Sheaf.-
    6. Step 3: Resolution of Rational Double Points.- References.- XII An Introduction to Arakelov Intersection Theory.-
    1. Definition of the Arakelov Intersection Pairing.-
    2. Metrized Line Bundles.-
    3. Volume Forms.-
    4. The Riemann-Roch Theorem and the Adjunction Formula.-
    5. The Hodge Index Theorem.- References.- XIII Minimal Models for Curves over Dedekind Rings.-
    1. Statement of the Minimal Models Theorem.-
    2. Factorization Theorem.-
    3. Statement of the Castelnuovo Criterion.-
    4. Intersection Theory and Proper and Total Transforms.-
    5. Exceptional Curves.- 5A. Intersection Properties.- 5B. Prime Divisors Satisfying the Castelnuovo Criterion.-
    6. Proof of the Castelnuovo Criterion.-
    7. Proof of the Minimal Models Theorem.- References.- XIV Local Heights on Curves.-
    1. Definitions and Notations.-
    2. Néron’s Local Height Pairing.-
    3. Construction of the Local Height Pairing.-
    4. The Canonical Height.-
    5. Local Heights for Divisors with Common Support.-
    6. Local Heights for Divisors of Arbitrary Degree.-
    7. Local Heights on Curves of Genus Zero.-
    8. Local Heights on Elliptic Curves.-
    9. Green’s Functions on the Upper Half-plane.-
    10. Local Heights on Mumford Curves.- References.- XV A Higher Dimensional Mordell Conjecture.-
    1. A Brief Introduction to Nevanlinna Theory.-
    2. Correspondence with Number Theory.-
    3. Higher Dimensional Nevanlinna Theory.-
    4. Consequences of the Conjecture.-
    5. Comparison with Faltings’ Proof.- References.