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Néron Models and Base Change

  • Lars Halvard Halle
  • Johannes Nicaise

Part of the Lecture Notes in Mathematics book series (LNM, volume 2156)

Table of contents

  1. Front Matter
    Pages i-x
  2. About This Book

    1. Front Matter
      Pages 1-1
    2. Lars Halvard Halle, Johannes Nicaise
      Pages 3-7
    3. Lars Halvard Halle, Johannes Nicaise
      Pages 9-19
    4. Lars Halvard Halle, Johannes Nicaise
      Pages 21-36
  3. Néron Component Groups of Semi-Abelian Varieties

    1. Front Matter
      Pages 37-37
    2. Lars Halvard Halle, Johannes Nicaise
      Pages 39-57
    3. Lars Halvard Halle, Johannes Nicaise
      Pages 59-86
  4. Chai and Yu’s Base Change Conductor and Edixhoven’s Filtration

    1. Front Matter
      Pages 87-87
    2. Lars Halvard Halle, Johannes Nicaise
      Pages 89-105
    3. Lars Halvard Halle, Johannes Nicaise
      Pages 107-116
  5. Applications to Motivic Zeta Functions

    1. Front Matter
      Pages 117-117
    2. Lars Halvard Halle, Johannes Nicaise
      Pages 119-128
    3. Lars Halvard Halle, Johannes Nicaise
      Pages 129-140
  6. Some Open Problems

    1. Front Matter
      Pages 141-141
    2. Lars Halvard Halle, Johannes Nicaise
      Pages 143-147
  7. Back Matter
    Pages 149-154

About this book

Introduction

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 a list of challenging open questions. This book is aimed towards researchers with a background in algebraic and arithmetic geometry.

Keywords

14K15, 14H40, 14G22, 14E18 Semi-abelian varieties Néron models Jacobians base change conductor motivic zeta functions

Authors and affiliations

  • Lars Halvard Halle
    • 1
  • Johannes Nicaise
    • 2
  1. 1.Dept. of Math. SciencesUniversity of CopenhagenCopenhagenDenmark
  2. 2.Dept. of MathematicsImperial College LondonLONDONUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-26638-1
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-26637-4
  • Online ISBN 978-3-319-26638-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site