Neron Models and Base Change

By Lars Halvard Halle and Johannes Nicaise

Presenting the first systematic treatment of the behavior of N ron models under ramified base change, this book can be read as an introduction to various subtle invariants and constructions related to N ron models of semi-abelian varieties, motivated by concrete research problems and complemented with explicit examples.

N ron models of abelian and semi-abelian varieties have become an indispensable tool in algebraic and arithmetic geometry since N ron introduced them in his seminal 1964 paper. Applications range from the theory of heights in Diophantine geometry to Hodge theory.

We focus specifically on N ron 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.

• Format: Paperback
• Language: English
• ISBN: 3319266373
• ISBN13: 9783319266374
• Release Date: March 2016
• Publisher: Springer
• Length: 151 Pages
• Weight: 0.53 lbs.
• Dimensions: 0.3" x 6.1" x 9.2"