Editors:
Invited articles by leading researchers 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
Graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections
Part of the book series: Progress in Mathematics (PM, volume 239)
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Table of contents (15 chapters)
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Front Matter
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.
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)Editors and Affiliations
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Korteweg-de Vries Instituut, Universiteit van Amsterdam, Amsterdam, The Netherlands
Gerard Geer, Ben Moonen
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Dipartimento di Matematica, Università di Roma “Tor Vergata”, Roma, Italy
René Schoof
Bibliographic Information
Book Title: Number Fields and Function Fields – Two Parallel Worlds
Editors: Gerard Geer, Ben Moonen, René Schoof
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/0-8176-4447-4
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2005
Hardcover ISBN: 978-0-8176-4397-3Published: 14 September 2005
eBook ISBN: 978-0-8176-4447-5Published: 24 November 2006
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XIII, 321
Topics: Algebraic Geometry, Number Theory, Mathematical Methods in Physics