TY - BOOK

T1 - Néron Models and Base Change

AU - Halle, Lars Halvard

AU - Nicaise, Johannes

PY - 2016

Y1 - 2016

N2 - Presenting the first systematic treatment of the behavior of Néron models under ramifiedbase change, this book can be read as an introduction to various subtle invariants andconstructions related to Néron models of semi-abelian varieties, motivated by concreteresearch problems and complemented with explicit examples.Néron models of abelian and semi-abelian varieties have become an indispensable toolin algebraic and arithmetic geometry since Néron introduced them in his seminal 1964paper. Applications range from the theory of heights in Diophantine geometry to Hodgetheory.We focus specifically on Néron component groups, Edixhoven’s filtration and the basechange conductor of Chai and Yu, and we study these invariants using various techniquessuch as models of curves, sheaves on Grothendieck sites and non-archimedeanuniformization. We then apply our results to the study of motivic zeta functions of abelianvarieties. The final chapter contains a list of challenging open questions. This book isaimed towards researchers with a background in algebraic and arithmetic geometry

AB - Presenting the first systematic treatment of the behavior of Néron models under ramifiedbase change, this book can be read as an introduction to various subtle invariants andconstructions related to Néron models of semi-abelian varieties, motivated by concreteresearch problems and complemented with explicit examples.Néron models of abelian and semi-abelian varieties have become an indispensable toolin algebraic and arithmetic geometry since Néron introduced them in his seminal 1964paper. Applications range from the theory of heights in Diophantine geometry to Hodgetheory.We focus specifically on Néron component groups, Edixhoven’s filtration and the basechange conductor of Chai and Yu, and we study these invariants using various techniquessuch as models of curves, sheaves on Grothendieck sites and non-archimedeanuniformization. We then apply our results to the study of motivic zeta functions of abelianvarieties. The final chapter contains a list of challenging open questions. This book isaimed towards researchers with a background in algebraic and arithmetic geometry

UR - https://www.springer.com/us/book/9783319266374

U2 - 10.1007/978-3-319-26638-1

DO - 10.1007/978-3-319-26638-1

M3 - Book

SN - 978-3-319-26637-4

T3 - Lecture Notes in Mathematics

BT - Néron Models and Base Change

PB - Springer Science+Business Media

ER -