Halle / Nicaise Néron Models and Base Change
1. Auflage 2016
ISBN: 978-3-319-26638-1
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 151 Seiten
Reihe: Mathematics and Statistics (R0)
ISBN: 978-3-319-26638-1
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
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Introduction.- Preliminaries.- Models of curves and the
Neron component series of a Jacobian.- Component groups and
non-archimedean uniformization.- The base change conductor and Edixhoven's ltration.-
The base change conductor and the Artin conductor.- Motivic zeta functions of
semi-abelian varieties.- Cohomological interpretation of the motivic zeta
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