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. BAckle; T. van den Bogaart; H. Brenner; F.
Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G.
Faltings; U. Hartl; R. de Jong; K. KAhler; U. KA1/4hn; J.C.
Lagarias; V. Maillot; R. Pink; D. Roessler; and A. Werner.
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