Read more
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.
Néron 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.
We focus specifically on Néron component groups, Edixhoven's 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 alist of challenging open questions. This book is aimed towardsresearchers with a background in algebraic and arithmetic geometry.
List of contents
Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 Introduction.- 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:11.0pt;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;}
Summary
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 alist of challenging open questions. This book is aimed towards
researchers with a background in algebraic and arithmetic geometry.
