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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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Arithmetic Algebraic Geometry
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Arithmetic Algebraic Geometry (Progress in Mathematics, Volume 89)
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Boston. Birkhäuser., 1991
ISBN 10: 3764335130
ISBN 13: 9783764335137
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Arithmetic Algebraic Geometry (Progress in Mathematics, Volume 89) G. van der Geer
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Arithmetic Algebraic Geometry (Progress in Mathematics)
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