Halle L.H., Nicaise J. Néron Models and Base Change

Springer International Publishing, 2016. — 151 p. — (Lecture Notes in Mathematics 2156). — ISBN: 978-3-319-26638-1; 978-3-319-26637-4.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.Preliminaries
Models of Curves and the Néron Component Series of a Jacobian
Component Groups and Non-Archimedean Uniformization
The Base Change Conductor and Edixhoven’s Filtration
The Base Change Conductor and the Artin Conductor
Motivic Zeta Functions of Semi-Abelian Varieties
Cohomological Interpretation of the Motivic Zeta Function
Some Open Problems