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Table of contents (10 chapters)
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About This Book
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Néron Component Groups of Semi-Abelian Varieties
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Chai and Yu’s Base Change Conductor and Edixhoven’s Filtration
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Applications to Motivic Zeta Functions
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Some Open Problems
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Néron Models and Base Change
Authors: Lars Halvard Halle, Johannes Nicaise
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-26638-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-26637-4Published: 03 March 2016
eBook ISBN: 978-3-319-26638-1Published: 02 March 2016
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 151
Topics: Algebraic Geometry, Number Theory