Number Fields and Function Fields – Two Parallel Worlds

Ever since the analogy between number fields and function fields was discovered in the 19th century it has been and remains a source of inspiration for new ideas. A deeper understanding of this correlation could have tremendous consequences for the search for a unified approach that has become a sort of Holy Grail. 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 include: G. Boeckle; T. van den Boogaart; H. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; G. Harder; U. Hartl; R. de Jong; K. Koehler; U. Kuehn; J. Lagarias; T. Oda; R. Pink; D. Roessler; U. Stuhler; and A. Werner.