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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