Nâeron Models / by Siegfried Bosch, Werner Lèutkebohmert, Michel Raynaud
| データ種別 | 電子書籍 |
|---|---|
| 版 | 1st ed. 1990. |
| 出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
| 出版年 | 1990 |
書誌詳細を非表示
| 書誌ID | OB00868576 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | 1. What Is a Nâeron Model? -- 1.1 Integral Points -- 1.2 Nâeron Models -- 1.3 The Local Case: Main Existence Theorem -- 1.4 The Global Case: Abelian Varieties -- 1.5 Elliptic Curves -- 1.6 Nâeron's Original Article -- 2. Some Background Material from Algebraic Geometry -- 2.1 Differential Forms -- 2.2 Smoothness -- 2.3 Henselian Rings -- 2.4 Flatness -- 2.5 S-Rational Maps -- 3. The Smoothening Process -- 3.1 Statement of the Theorem -- 3.2 Dilatation -- 3.3 Nâeron's Measure for the Defect of Smoothness -- 3.4 Proof of the Theorem -- 3.5 Weak Nâeron Models -- 3.6 Algebraic Approximation of Formal Points -- 4. Construction of Birational Group Laws -- 4.1 Group Schemes -- 4.2 Invariant Differential Forms -- 4.3 R-Extensions of K-Group Laws -- 4.4 Rational Maps into Group Schemes -- 5. From Birational Group Laws to Group Schemes -- 5.1 Statement of the Theorem -- 5.2 Strict Birational Group Laws -- 5.3 Proof of the Theorem for a Strictly Henselian Base -- 6. Descent -- 6.1 The General Problem -- 6.2 Some Standard Examples of Descent -- 6.3 The Theorem of the Square -- 6.4 The Quasi-Projectivity of Torsors -- 6.5 The Descent of Torsors -- 6.6 Applications to Birational Group Laws -- 6.7 An Example of Non-Effective Descent -- 7. Properties of Nâeron Models -- 7.1 A Criterion -- 7.2 Base Change and Descent -- 7.3 Isogenies -- 7.4 Semi-Abelian Reduction -- 7.5 Exactness Properties -- 7.6 Weil Restriction -- 8. The Picard Functor -- 8.1 Basics on the Relative Picard Functor -- 8.2 Representability by a Scheme -- 8.3 Representability by an Algebraic Space -- 8.4 Properties -- 9. Jacobians of Relative Curves -- 9.1 The Degree of Divisors -- 9.2 The Structure of Jacobians -- 9.3 Construction via Birational Group Laws -- 9.4 Construction via Algebraic Spaces -- 9.5 Picard Functor and Nâeron Models of Jacobians -- 9.6 The Group of Connected Components of a Nâeron Model -- 9.7 Rational Singularities -- 10. Nâeron Models of Not Necessarily Proper Algebraic Groups -- 10.1 Generalities -- 10.2 The Local Case -- 10.3 The Global Case. License restrictions may limit access Summary: Nâeron models were invented by A. Nâeron in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithmeticians and algebraic geometers have applied the theory of Nâeron models with great success. Quite recently, new developments in arithmetic algebraic geometry have prompted a desire to understand more about Nâeron models, and even to go back to the basics of their construction. The authors have taken this as their incentive to present a comprehensive treatment of Nâeron models. This volume of the renowned "Ergebnisse" series provides a detailed demonstration of the construction of Nâeron models from the point of view of Grothendieck's algebraic geometry. In the second part of the book the relationship between Nâeron models and the relative Picard functor in the case of Jacobian varieties is explained. The authors helpfully remind the reader of some important standard techniques of algebraic geometry. A special chapter surveys the theory of the Picard functor |
| 著者標目 | *Bosch, Siegfried Lèutkebohmert, Werner Raynaud, Michel SpringerLink (Online service) |
| 統一書名標目 | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, |
| 件 名 | LCSH:Geometry, algebraic FREE:Algebraic Geometry |
| 分 類 | LCC:QA564-609 DC23:516.35 |
| 巻冊次 | ISBN:9783642514388 RefWorks出力（各巻） print ; ISBN:9783642080739 RefWorks出力（各巻） print ; ISBN:9783540505877 RefWorks出力（各巻） print ; ISBN:9783642514395 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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