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Arithmetic and Geometry over Local Fields

VIASM 2018

  • Book
  • © 2021

Overview

Editors:
  1. Bruno Anglès

    1. Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, Université de Caen Basse-Normandie, Caen, France

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  2. Tuan Ngo Dac

    1. Institut Camille Jordan, UMR 5208, Claude Bernard University Lyon 1, Villeurbanne, France

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    You can also search for this editor in PubMed   Google Scholar

  • Designed to enable young mathematicians to tackle concrete research problems
  • Gives an overview of recent developments in arithmetic and geometry over local fields
  • Provides a self-contained course on Drinfeld modules and non-Archimedean analytic geometry

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2275)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Some Elements on Berthelot’s Arithmetic \({\mathscr {D}}\)-Modules

    • Daniel Caro
    Pages 1-28

  3. Difference Galois Theory for the “Applied” Mathematician

    • Lucia Di Vizio
    Pages 29-59

  4. Igusa’s Conjecture on Exponential Sums Modulo p m and the Local-Global Principle

    • Kien Huu Nguyen
    Pages 61-92

  5. From the Carlitz Exponential to Drinfeld Modular Forms

    • Federico Pellarin
    Pages 93-177

  6. Berkovich Curves and Schottky Uniformization I: The Berkovich Affine Line

    • Jérôme Poineau, Daniele Turchetti
    Pages 179-223

  7. Berkovich Curves and Schottky Uniformization II: Analytic Uniformization of Mumford Curves

    • Jérôme Poineau, Daniele Turchetti
    Pages 225-279

  8. On the Stark Units of Drinfeld Modules

    • Floric Tavares Ribeiro
    Pages 281-324

  9. Back Matter

    Pages 325-326
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Keywords

About this book

This volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program "Arithmetic and geometry of local and global fields" which took place at the Vietnam Institute of Advanced Study in Mathematics (VIASM) from June to August 2018.

The authors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics.

Editors and Affiliations

  • Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, Université de Caen Basse-Normandie, Caen, France

    Bruno Anglès

  • Institut Camille Jordan, UMR 5208, Claude Bernard University Lyon 1, Villeurbanne, France

    Tuan Ngo Dac

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