Neron Models And Base Change (lecture Notes In Mathematics)
by Lars Halvard Halle /
2016 / English / PDF
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Presenting the first systematic treatment of the behavior of Nron models under ramified base change, this book can be read as an introduction to various subtle invariants and constructions related to Nron models of semi-abelian varieties, motivated by concrete research problems and complemented with explicit examples.
Nron models of abelian and semi-abelian varieties have become an indispensable tool in algebraic and arithmetic geometry since Nron introduced them in his seminal 1964 paper. Applications range from the theory of heights in Diophantine geometry to Hodge theory.
We focus specifically on Nron component groups, Edixhovens 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.
