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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 alist of challenging open questions. This book is aimed towards
researchers with a background in algebraic and arithmetic geometry.
Series
Edition
Language
Place of publication
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Product notice
Illustrations
ISBN-13
978-3-319-26638-1 (9783319266381)
DOI
10.1007/978-3-319-26638-1
Schweitzer Classification
Normal
0
false
false
false
EN-US
X-NONE
X-NONE
MicrosoftInternetExplorer4
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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