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Number Fields and Function Fields—Two Parallel Worlds

  • Gerard van der Geer
  • Ben Moonen
  • René Schoof

Part of the Progress in Mathematics book series (PM, volume 239)

About this book

Introduction

Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject.

As a deeper understanding of this analogy could have tremendous consequences, the search for a unified approach has become a sort of Holy Grail. The arrival of Arakelov's new geometry that tries to put the archimedean places on a par with the finite ones gave a new impetus and led to spectacular success in Faltings' hands. There are numerous further examples where ideas or techniques from the more geometrically-oriented world of function fields have led to new insights in the more arithmetically-oriented world of number fields, or vice versa.

These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives.

This volume is aimed at a wide audience of graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections.

Contributors: G. Böckle; T. van den Bogaart; H. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; U. Hartl; R. de Jong; K. Köhler; U. Kühn; J.C. Lagarias; V. Maillot; R. Pink; D. Roessler; and A. Werner.

Keywords

Arithmetic Finite Grad Invariant algebra finite field function geometry

Editors and affiliations

  • Gerard van der Geer
    • 1
  • Ben Moonen
    • 1
  • René Schoof
    • 2
  1. 1.Korteweg-de Vries InstituutUniversiteit van AmsterdamAmsterdamThe Netherlands
  2. 2.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/0-8176-4447-4
  • Copyright Information Birkhäuser Boston 2005
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4397-3
  • Online ISBN 978-0-8176-4447-5
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site