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