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ISBN: 9783540505877

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… Altro …

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ISBN: 9783540505877

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 geomet… Altro …

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Néron Models: 21 (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: 21 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 21) - copertina rigida, flessible

1990

ISBN: 9783540505877

Springer, Hardcover, Auflage: 1990, 338 Seiten, Publiziert: 1990-04-12T00:00:01Z, Produktgruppe: Book, Hersteller-Nr.: 4 black & white illustrations, 1.92 kg, Verkaufsrang: 2590945, Books… Altro …

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Bosch, Siegfried; Raynaud, Michel; Lütkebohmert, Werner:
Néron Models - copertina rigida, flessible

1990, ISBN: 3540505873

1990 Gebundene Ausgabe Mathematik / Höhere Mathematik, AbelscheVarietäten; Algebra; AlgebraischeGruppen; Arithmetic; Invariant; Jacobi-Varietäten; Picard-Functor; Geometry; proof; theor… Altro …

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Siegfried Bosch/ Werner Lütkebohmert/ Michel Raynaud:
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ISBN: 9783540505877

*Néron Models* - Auflage 1990 / gebundene Ausgabe für 170.99 € / Aus dem Bereich: Bücher, Wissenschaft, Mathematik Medien > Bücher nein Buch (gebunden) Hardcover;Naturwissenschaften, Medi… Altro …

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Dettagli del libro
Néron Models Siegfried Bosch Author
Autore:
Titolo:
ISBN:

3540505873


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.

Informazioni dettagliate del libro - Néron Models Siegfried Bosch Author


EAN (ISBN-13): 9783540505877
ISBN (ISBN-10): 3540505873
Copertina rigida
Copertina flessibile
Anno di pubblicazione: 1990
Editore: Springer Berlin Heidelberg Core >2 >T
325 Pagine
Peso: 0,791 kg

Libro nella banca dati dal 2008-06-28T00:20:49+02:00 (Rome)
Pagina di dettaglio ultima modifica in 2024-03-19T09:07:55+01:00 (Rome)
ISBN/EAN: 3540505873

ISBN - Stili di scrittura alternativi:
3-540-50587-3, 978-3-540-50587-7
Stili di scrittura alternativi e concetti di ricerca simili:
Autore del libro : michel, bosch raynaud lütkebohmert, werner bösch, siegfried bosch, bosch lutkebohmert, lütke, grothendieck
Titolo del libro: surveys modern mathematics, neron models, ergebnisse, mathematik der, grenzgebiete, nero, bosch

Dati dell'editore

Autore: Siegfried Bosch; Werner Lütkebohmert; Michel Raynaud
Titolo: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics; Néron Models
Editore: Springer; Springer Berlin
328 Pagine
Anno di pubblicazione: 1990-04-12
Berlin; Heidelberg; DE
Lingua: Inglese
181,89 € (DE)
186,99 € (AT)
201,00 CHF (CH)
Available
X, 328 p.

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

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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