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Néron Models and Base Change
Taschenbuch von Johannes Nicaise (u. a.)
Sprache: Englisch

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Beschreibung
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 alist of challenging open questions. This book is aimed towards
researchers with a background in algebraic and arithmetic geometry.
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 alist of challenging open questions. This book is aimed towards
researchers with a background in algebraic and arithmetic geometry.
Inhaltsverzeichnis
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Introduction.- Preliminaries.- Models of curves and the
Neron component series of a Jacobian.- Component groups and
non-archimedean uniformization.- The base change conductor and Edixhoven's ltration.-
The base change conductor and the Artin conductor.- Motivic zeta functions of
semi-abelian varieties.- Cohomological interpretation of the motivic zeta
function.

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Details
Erscheinungsjahr: 2016
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 164
Reihe: Lecture Notes in Mathematics
Inhalt: x
151 S.
ISBN-13: 9783319266374
ISBN-10: 3319266373
Sprache: Englisch
Herstellernummer: 978-3-319-26637-4
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Nicaise, Johannes
Halle, Lars Halvard
Auflage: 1st ed. 2016
Hersteller: Springer International Publishing
Springer International Publishing AG
Lecture Notes in Mathematics
Maße: 235 x 155 x 10 mm
Von/Mit: Johannes Nicaise (u. a.)
Erscheinungsdatum: 03.03.2016
Gewicht: 0,26 kg
preigu-id: 104166279
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Introduction.- Preliminaries.- Models of curves and the
Neron component series of a Jacobian.- Component groups and
non-archimedean uniformization.- The base change conductor and Edixhoven's ltration.-
The base change conductor and the Artin conductor.- Motivic zeta functions of
semi-abelian varieties.- Cohomological interpretation of the motivic zeta
function.

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Details
Erscheinungsjahr: 2016
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 164
Reihe: Lecture Notes in Mathematics
Inhalt: x
151 S.
ISBN-13: 9783319266374
ISBN-10: 3319266373
Sprache: Englisch
Herstellernummer: 978-3-319-26637-4
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Nicaise, Johannes
Halle, Lars Halvard
Auflage: 1st ed. 2016
Hersteller: Springer International Publishing
Springer International Publishing AG
Lecture Notes in Mathematics
Maße: 235 x 155 x 10 mm
Von/Mit: Johannes Nicaise (u. a.)
Erscheinungsdatum: 03.03.2016
Gewicht: 0,26 kg
preigu-id: 104166279
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