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Néron Models and Base Change

  • Book
  • © 2016

Overview

Authors:
  1. Lars Halvard Halle

    1. Dept. of Math. Sciences, University of Copenhagen, Copenhagen, Denmark

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  2. Johannes Nicaise

    1. Dept. of Mathematics, Imperial College London, LONDON, United Kingdom

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
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  2. About This Book

    1. Front Matter

      Pages 1-1
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    2. Content of This Book

      • Lars Halvard Halle, Johannes Nicaise
      Pages 3-7

    3. Introduction

      • Lars Halvard Halle, Johannes Nicaise
      Pages 9-19

    4. Preliminaries

      • Lars Halvard Halle, Johannes Nicaise
      Pages 21-36

  3. Néron Component Groups of Semi-Abelian Varieties

    1. Front Matter

      Pages 37-37
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    2. Models of Curves and the Néron Component Series of a Jacobian

      • Lars Halvard Halle, Johannes Nicaise
      Pages 39-57

    3. Component Groups and Non-Archimedean Uniformization

      • 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
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    2. The Base Change Conductor and Edixhoven’s Filtration

      • Lars Halvard Halle, Johannes Nicaise
      Pages 89-105

    3. The Base Change Conductor and the Artin Conductor

      • Lars Halvard Halle, Johannes Nicaise
      Pages 107-116

  5. Applications to Motivic Zeta Functions

    1. Front Matter

      Pages 117-117
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    2. Motivic Zeta Functions of Semi-Abelian Varieties

      • Lars Halvard Halle, Johannes Nicaise
      Pages 119-128

    3. Cohomological Interpretation of the Motivic Zeta Function

      • Lars Halvard Halle, Johannes Nicaise
      Pages 129-140

  6. Some Open Problems

    1. Front Matter

      Pages 141-141
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    2. Some Open Problems

      • Lars Halvard Halle, Johannes Nicaise
      Pages 143-147

  7. Back Matter

    Pages 149-154
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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

  • Dept. of Math. Sciences, University of Copenhagen, Copenhagen, Denmark

    Lars Halvard Halle

  • Dept. of Mathematics, Imperial College London, LONDON, United Kingdom

    Johannes Nicaise

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

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