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NéRON MODELS AND BASE CHANGE IBD

JOHANNES NICAISE / LARS HALVARD HALLE
SPRINGER
03 / 2016
9783319266374
Inglés

Sinopsis

Presentingthe first systematic treatment of the behavior of Néron models under ramifiedbase change, this book can be read as an introduction to various subtleinvariants and constructions related to Néron models of semi-abelian varieties,motivated by concrete research problems and complemented with explicitexamples.ááNéron models of abelian andsemi-abelian varieties have become an indispensable tool in algebraic andarithmetic geometry since Néron introduced them in his seminal 1964 paper.Applications range from the theory of heights in Diophantine geometry to Hodgetheory.áWe focus specifically on Néron component groups, EdixhovenâÇÖs 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.