[PDF] Neron Models eBook

Author : Siegfried Bosch
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 22,89 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642514383

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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.

Author : Lars Halvard Halle
Publisher : Springer
Page : 154 pages
File Size : 30,45 MB
Release : 2016-03-02
Category : Mathematics
ISBN : 3319266381

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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.

Author : Siegfried Bosch
Publisher :
Page : 340 pages
File Size : 45,49 MB
Release : 1990-04-12
Category :
ISBN : 9783642514395

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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.

Author : Gerard van der Geer
Publisher : Birkhäuser
Page : 526 pages
File Size : 34,29 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 303488303X

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Abelian varieties and their moduli are a topic of increasing importance in today`s mathematics, applications ranging from algebraic geometry and number theory to mathematical physics. This collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field.

Author : Thomas Haines
Publisher : Cambridge University Press
Page : 341 pages
File Size : 12,86 MB
Release : 2020-02-20
Category : Mathematics
ISBN : 1108704867

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This volume forms the sequel to "On the stabilization of the trace formula", published by International Press of Boston, Inc., 2011

Author : Barbara Fantechi
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 50,13 MB
Release : 2005
Category : Mathematics
ISBN : 0821842455

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Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.

Author : Luis Dieulefait
Publisher : Cambridge University Press
Page : 539 pages
File Size : 24,80 MB
Release : 2015-10-08
Category : Mathematics
ISBN : 1316381447

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The 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on Serre's conjecture and on rational points on algebraic varieties. The resulting proceedings volume provides a modern overview of the subject for graduate students in arithmetic geometry and Diophantine geometry. It is also essential reading for any researcher wishing to keep abreast of the latest developments in the field. Highlights include Tim Browning's survey on applications of the circle method to rational points on algebraic varieties and Per Salberger's chapter on rational points on cubic hypersurfaces.

Author : Allan Adler
Publisher : Springer
Page : 205 pages
File Size : 49,1 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540496092

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This is a book aimed at researchers and advanced graduate students in algebraic geometry, interested in learning about a promising direction of research in algebraic geometry. It begins with a generalization of parts of Mumford's theory of the equations defining abelian varieties and moduli spaces. It shows through striking examples how one can use these apparently intractable systems of equations to obtain satisfying insights into the geometry and arithmetic of these varieties. It also introduces the reader to some aspects of the research of the first author into representation theory and invariant theory and their applications to these geometrical questions.

Author : B. Mazur
Publisher : Springer
Page : 142 pages
File Size : 47,12 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540379339

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Author : Haruzo Hida
Publisher : World Scientific
Page : 375 pages
File Size : 23,86 MB
Release : 2000-09-27
Category : Mathematics
ISBN : 9814492892

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This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction.