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9780817635138: Arithmetic Algebraic Geometry: 89 (Progress in Mathematics, 89)
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ISBN 10: 0817635130 ISBN 13: 9780817635138
Editorial: Birkhäuser, 1990

Sinopsis

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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De la contraportada

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.

Inspired by these exciting developments, the editors organized a meeting at Texel in 1989 and invited a number of mathematicians to write papers for this volume. Some of these papers were presented at the meeting; others arose from the discussions that took place. They were all chosen for their quality and relevance to the application of algebraic geometry to arithmetic problems.

Topics include: arithmetic surfaces, Chjerm functors, modular curves and modular varieties, elliptic curves, Kolyvagin’s work, K-theory and Galois representations. Besides the research papers, there is a letter of Parshin and a paper of Zagier with is interpretations of the Birch-Swinnerton-Dyer Conjecture.

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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Editorial
Birkhäuser
Año de publicación
1990
Idioma
Inglés
ISBN 10 
0817635130
ISBN 13 
9780817635138
Encuadernación
Tapa dura
Número de páginas
444
Editor
Geer G. Van Der, Oort F., Steenbrink J.H.M.
Contacto del fabricante
Springer Nature Customer Service Center GmbH
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