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Progress in Mathematics

Number Fields and Function Fields – Two Parallel Worlds

Editors: van der Geer, Gerard, Moonen, B.J.J, Schoof, René (Eds.)

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Hardcover 80,03 €
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  • ISBN 978-0-8176-4397-3
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About this book

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.

Reviews

From the reviews:

“I thoroughly enjoyed the book; referring to it now and then through the various pages has been a wonderful experience. … It is a stimulating and well-researched volume, aimed at a wide audience of gradute students, mathematicians, and researchers interested in geometry and arithmetic and their connections. In short, it places a most engaging progress in mathematics volume in the hands of the target audience who will enjoy, not just profit from, the different aspects of the involved parallelism.” (Current Engineering Practice, Vol. 48, 2005-2006)

Table of contents (2 chapters)

  • Arithmetic over Function Fields: A Cohomological Approach

    Gebhard Böckle

    Pages 1-38

    Preview Buy Chapter 30,19 €
  • Line Bundles and p-Adic Characters

    Christopher Deninger, Annette Werner

    Pages 101-131

    Preview Buy Chapter 30,19 €

Buy this book

eBook 64,99 €
price for Spain (gross)
  • ISBN 978-0-8176-4447-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 80,03 €
price for Spain (gross)
  • ISBN 978-0-8176-4397-3
  • with online files
  • Free shipping for individuals worldwide
  • This title is currently reprinting. You can pre-order your copy now.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Number Fields and Function Fields – Two Parallel Worlds
Editors
  • Gerard van der Geer
  • B.J.J Moonen
  • René Schoof
Series Title
Progress in Mathematics
Series Volume
239
Copyright
2005
Publisher
Birkhäuser Basel
Copyright Holder
The Editor(s) (if applicable) and The Author(s) 2018
eBook ISBN
978-0-8176-4447-5
DOI
10.1007/0-8176-4447-4
Hardcover ISBN
978-0-8176-4397-3
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XIII, 321
Topics