Arithmetic algebraic geometry is in a fascinating stage of
growth, providing a rich variety of applications of new tools to
both old and new problems. Representative of these recent
developments is the notion of Arakelov geometry, a way of
"completing" a variety over the ring of integers of a number field
by adding fibres over the Archimedean places. Another is the
appearance of the relations between arithmetic geometry and
Nevanlinna theory, or more precisely between diophantine
approximation theory and the value distribution theory of
holomorphic maps. Research mathematicians and graduate students in
algebraic geometry and number theory will find a valuable and
lively view of the field in this state-of-the-art selection.
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