Nron Models and Base Change [Paperback]

Presentingthe first systematic treatment of the behavior of N?ron models under ramifiedbase change, this book can be read as an introduction to various subtleinvariants and constructions related to N?ron models of semi-abelian varieties,motivated by concrete research problems and complemented with explicitexamples.  

N?ron models of abelian andsemi-abelian varieties have become an indispensable tool in algebraic andarithmetic geometry since N?ron introduced them in his seminal 1964 paper.Applications range from the theory of heights in Diophantine geometry to Hodgetheory. 

We focus specifically on N?ron component groups, Edixhovens 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.

Normal0falsefalsefalseEN-USX-NONEX-NONEMicrosoftInternetExplorer4Introduction.- Preliminaries.- Models of curves and theNeron component series of a Jacobian.- Component groups andnon-archimedean uniformization.- The base change conductor and Edixhoven's ltration.-The base change conductor and the Artin conductor.- Motivic zeta functions ofsemi-abelian varieties.- Cohomological interpretation of the motivic zetafunction./* 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.lS²