Number Fields and Function Fields: Two Parallel Worlds (Progress in Mathematics) (Progress in Mathematics, 239)

Number Fields and Function Fields: Two Parallel Worlds (Progress in Mathematics) (Progress in Mathematics, 239)
by: Gerard B. M. van der Geer (Editor),BJJ Moonen (Editor),René Schoof (Editor)&0more
Publisher: Birkhäuser
Edition: 2005th
Publication Date: 2005/9/14
Language: English
Print Length: 334 pages
ISBN-10: 0817643974
ISBN-13: 9780817643973
Book Description
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.
About the Author
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. Read more