TY  - BOOK
AU  - Halle,Lars Halvard
AU  - Nicaise,Johannes
TI  - Neron models and base change
T2  - Lecture notes in mathematics
SN  - 9783319266374 
U1  - 516.35 23
PY  - 2016///
CY  - Switzerland
PB  - Springer
KW  - Neron models.
N1  - Includes bibliographical references; 1. Content of this book --
2. Introduction --
3. Preliminaries --
4. Models of Curves and the Néron Component Series of a Jacobian --
5. Component Groups and Non-Archimedean Uniformization --
6. The Base Change Conductor and Edixhoven's Filtration --
7. The Base Change Conductor and the Artin Conductor --
8. Motivic Zeta Functions of Semi-Abelian Varieties --
9. Cohomological Interpretation of the Motivic Zeta Function --
10. Some Open Problems
N2  - 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
ER  -