Néron Models and Base Change Normal 0 false false false EN US X NONE X NONE MicrosoftInternetExplorer4 Introduction Preliminaries Models of curves and the Neron component series of a Jacobian Component groups and non archimedean uniformization The base change conductor and Edixhovens ltration The base change conductor and the Artin conductor Motivic zeta functions of semi abelian varieties Cohomological interpretation of the motivic zeta function. * Style Definitions * table.MsoNormalTable {mso style name: Table Normal ; mso tstyle rowband size:0; mso tstyle colband size:0; mso style noshow:yes; mso style priority:99; mso style qformat:yes; mso style parent: ; mso padding alt:0in 5.4pt 0in 5.4pt; mso para margin top:0in; mso para margin right:0in; mso para margin bottom:10.0pt; mso para margin left:0in; line height:115%; mso pagination:widow orphan; font size:11.0pt; font family: Calibri sans serif ; mso ascii font family:Calibri; mso ascii theme font:minor latin; mso fareast font family: Times New Roman ; mso fareast theme font:minor fareast; mso hansi font family:Calibri; mso hansi theme font:minor latin; mso bidi font family: Times New Roman ; mso bidi theme font:minor bidi;}. Presenting the first systematic treatment of the behavior of Néron models under ramified base change this book can be read as an introduction to various subtle invariants and constructions related to Néron models of semi abelian varieties motivated by concrete research problems and complemented with explicit examples. Néron models of abelian and semi abelian varieties have become an indispensable tool in algebraic and arithmetic geometry since Néron introduced them in his seminal 1964 paper. Applications range from the theory of heights in Diophantine geometry to Hodge theory. We focus specifically on Néron 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 a list of challenging open questions. This book is aimed towards researchers with a background in algebraic and arithmetic geometry.