Lars Halvard Halle, Johannes Nicaise

Néron Models and Base Change (eBook, PDF)

• Format: PDF

Produktbeschreibung

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 resultsto 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.

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Produktdetails

• Verlag: Springer Nature Switzerland
• Seitenzahl: 151
• Erscheinungstermin: 2. März 2016
• Englisch
• ISBN-13: 9783319266381
• Artikelnr.: 44897746

Inhaltsangabe

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;}