Lars Halvard Halle, Johannes Nicaise Neron Models and Base Change

Annotation

Presentingthe first systematic treatment of the behavior of Nron models under ramifiedbase change, this book can be read as an introduction to various subtleinvariants and constructions related to Nron models of semi-abelian varieties,motivated by concrete research problems and complemented with explicitexamples.  Nron models of abelian andsemi-abelian varieties have become an indispensable tool in algebraic andarithmetic geometry since Nron introduced them in his seminal 1964 paper. Applications range from the theory of heights in Diophantine geometry to Hodgetheory. We focus specifically on Nron component groups, Edixhoven's filtrationand the base change conductor of Chai and Yu, and we study these invariantsusing various techniques such as models of curves, sheaves on Grothendiecksites and non-archimedean uniformization. We then apply our results to thestudy of motivic zeta functions of abelian varieties. The final chaptercontains a list of challenging open questions. This book is aimed towardsresearchers with a background in algebraic and arithmetic geometry.