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Néron Models - Siegfried Bosch
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Siegfried Bosch:

Néron Models - Paperback

2010, ISBN: 3642080731

[EAN: 9783642080739], Neubuch, [SC: 0.0], [PU: Springer Berlin Heidelberg], ABELSCHEVARIETÄTEN; ALGEBRA; ALGEBRAISCHEGRUPPEN; ARITHMETIC; INVARIANT; JACOBI-VARIETÄTEN; PICARD-FUNCTOR; GEO… More...

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Neron Models - new book

ISBN: 9783642080739

Néron models were invented by A. Néron in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithmeticians and algebr… More...

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Néron Models (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 21) - Bosch, Siegfried, Lütkebohmert, Werner, Raynaud, Michel
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Bosch, Siegfried, Lütkebohmert, Werner, Raynaud, Michel:
Néron Models (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 21) - Paperback

2010

ISBN: 9783642080739

Springer, Paperback, Auflage: Softcover reprint of the original 1st ed. 1990, 338 Seiten, Publiziert: 2010-12-01T00:00:01Z, Produktgruppe: Book, Hersteller-Nr.: biography, 0.67 kg, Verkau… More...

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Néron Models - Bosch, Siegfried; Raynaud, Michel; Lütkebohmert, Werner
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Bosch, Siegfried; Raynaud, Michel; Lütkebohmert, Werner:
Néron Models - Paperback

2010, ISBN: 3642080731

Softcover reprint of the original 1st ed. 1990 Kartoniert / Broschiert Geometry; proof; theorem; AbelscheVarietäten; Algebra; AlgebraischeGruppen; Arithmetic; Invariant; Picard-Functor;… More...

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Néron Models - Siegfried Bosch; Werner Lütkebohmert; Michel Raynaud
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Siegfried Bosch; Werner Lütkebohmert; Michel Raynaud:
Néron Models - Paperback

2010, ISBN: 9783642080739

Buch, Softcover, Softcover reprint of the original 1st ed. 1990, [PU: Springer Berlin], Springer Berlin, 2010

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Details of the book
Néron Models
Author:
Title:
ISBN:

3642080731


Néron models were invented by A. Néron 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 Néron models with great success. Quite recently, new developments in arithmetic algebraic geometry have prompted a desire to understand more about Néron 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 Néron models. This volume of the renowned "Ergebnisse" series provides a detailed demonstration of the construction of Néron models from the point of view of Grothendieck's algebraic geometry. In the second part of the book the relationship between Néron 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.

Details of the book - Néron Models


EAN (ISBN-13): 9783642080739
ISBN (ISBN-10): 3642080731
Hardcover
Paperback
Publishing year: 2010
Publisher: Springer Berlin
340 Pages
Weight: 0,606 kg
Language: eng/Englisch

Book in our database since 2010-07-11T09:28:28-04:00 (New York)
Detail page last modified on 2023-06-29T05:43:39-04:00 (New York)
ISBN/EAN: 3642080731

ISBN - alternate spelling:
3-642-08073-1, 978-3-642-08073-9
Alternate spelling and related search-keywords:
Book author: bosch raynaud lütkebohmert, werner bösch, siegfried bosch, werner best, bosch lutkebohmert, grothendieck
Book title: mathematik, neron models, ergebnisse, surveys modern mathematics, nero, bosch

Information from Publisher

Author: Siegfried Bosch; Werner Lütkebohmert; Michel Raynaud
Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics; Néron Models
Publisher: Springer; Springer Berlin
328 Pages
Publishing year: 2010-12-01
Berlin; Heidelberg; DE
Printed / Made in
Language: English
181,89 € (DE)
186,99 € (AT)
201,00 CHF (CH)
POD
X, 328 p.

BC; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Algebraische Geometrie; Verstehen; Abelsche Varietäten; Algebra; Algebraische Gruppen; Arithmetic; Invariant; Jacobi-Varietäten; Picard-Functor; geometry; proof; theorem; Algebraic Geometry; BB

1. What Is a Néron Model?.- 1.1 Integral Points.- 1.2 Néron Models.- 1.3 The Local Case: Main Existence Theorem.- 1.4 The Global Case: Abelian Varieties.- 1.5 Elliptic Curves.- 1.6 Néron’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 Néron’s Measure for the Defect of Smoothness.- 3.4 Proof of the Theorem.- 3.5 Weak Néron 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 Néron 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 Néron Models of Jacobians.- 9.6 The Group ofConnected Components of a Néron Model.- 9.7 Rational Singularities.- 10. Néron Models of Not Necessarily Proper Algebraic Groups.- 10.1 Generalities.- 10.2 The Local Case.- 10.3 The Global Case.

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