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Table of contents (20 chapters)
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Front Matter
Keywords
About this book
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.
Editors and Affiliations
Bibliographic Information
Book Title: Arithmetic Algebraic Geometry
Editors: G. Geer, F. Oort, J. Steenbrink
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-1-4612-0457-2
Publisher: Birkhäuser Boston, MA
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1991
Hardcover ISBN: 978-0-8176-3513-8Published: 01 December 1990
Softcover ISBN: 978-1-4612-6769-0Published: 11 October 2012
eBook ISBN: 978-1-4612-0457-2Published: 06 December 2012
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: X, 444
Topics: Algebraic Geometry, Algebra, Number Theory