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Néron Models

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 383/5 ( reviews)

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Book Synopsis Néron Models by : Siegfried Bosch

Download or read book Néron Models written by Siegfried Bosch. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Néron Models and Base Change

2016-03-02 Mathematics
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Release : 2016-03-02
Genre : Mathematics
Kind : eBook
Book Rating : 381/5 ( reviews)

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Book Synopsis Néron Models and Base Change by : Lars Halvard Halle

Download or read book Néron Models and Base Change written by Lars Halvard Halle. This book was released on 2016-03-02. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the first systematic treatment of the behavior of Néron models under ramified base change, this book can be read as an introduction to various subtle invariants and constructions related to Néron models of semi-abelian varieties, motivated by concrete research problems and complemented with explicit examples. Néron models of abelian and semi-abelian varieties have become an indispensable tool in algebraic and arithmetic geometry since Néron introduced them in his seminal 1964 paper. Applications range from the theory of heights in Diophantine geometry to Hodge theory. We focus specifically on Néron component groups, Edixhoven’s filtration and the base change conductor of Chai and Yu, and we study these invariants using various techniques such as models of curves, sheaves on Grothendieck sites and non-archimedean uniformization. We then apply our results to the study of motivic zeta functions of abelian varieties. The final chapter contains a list of challenging open questions. This book is aimed towards researchers with a background in algebraic and arithmetic geometry.

Neron Models

1990-04-12
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Release : 1990-04-12
Genre :
Kind : eBook
Book Rating : 395/5 ( reviews)

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Book Synopsis Neron Models by : Siegfried Bosch

Download or read book Neron Models written by Siegfried Bosch. This book was released on 1990-04-12. Available in PDF, EPUB and Kindle. Book excerpt: Neron models were invented by A. Neron 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 Neron models with great success. Quite recently, new developments in arithmetic algebraic geometry have prompted a desire to understand more about Neron 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 Neron models. This volume of the renowned "Ergebnisse" series provides a detailed demonstration of the construction of Neron models from the point of view of Grothendieck's algebraic geometry. In the second part of the book the relationship between Neron 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.

Library of Congress Subject Headings

2009 Subject headings, Library of Congress
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Release : 2009
Genre : Subject headings, Library of Congress
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Library of Congress Subject Headings by : Library of Congress

Download or read book Library of Congress Subject Headings written by Library of Congress. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt:

Library of Congress Subject Headings

2009 Subject headings, Library of Congress
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Release : 2009
Genre : Subject headings, Library of Congress
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Library of Congress Subject Headings by : Library of Congress. Cataloging Policy and Support Office

Download or read book Library of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt:

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