| Number Fields and Function Fields - Two Parallel Worlds 2005 Edition Contributor(s): Van Der Geer, Gerard B. M. (Editor), Moonen, Bjj (Editor), Schoof, René (Editor) |
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ISBN: 0817643974 ISBN-13: 9780817643973 Publisher: Birkhauser OUR PRICE: $123.49 Product Type: Hardcover Published: September 2005 Annotation: 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. Bckle; T. van den Bogaart; H. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; U. Hartl; R. de Jong; K. Khler; U. Khn; J.C. Lagarias; V. Maillot; R. Pink; D. Roessler; and A. Werner. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Algebraic - Mathematics | Number Theory - Science | Physics - Mathematical & Computational |
| Dewey: 512.3 |
| LCCN: 2006530652 |
| Series: Progress in Mathematics |
| Physical Information: 0.79" H x 6.62" W x 9.34" (1.30 lbs) 321 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections |