Arithmetic algebraic geometry /

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 o...

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Bibliographic Details
Corporate Author: SpringerLink (Online service)
Other Authors: Geer, Gerard van der, Oort, Frans, 1935-, Steenbrink, J. H. M.
Format: eBook
Language:English
Published: Boston : Birkhäuser, 1991.
Series:Progress in mathematics (Boston, Mass.) ; v. 89.
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Online Access:Connect to the full text of this electronic book
Description
Summary: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.
Item Description:Papers from the conference Arithmetic Algebraic Geometry, Texel '89, held on Texel Island, Apr. 1989.
Electronic resource.
Physical Description:1 online resource (x, 444 pages) : illustrations.
Format:Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Bibliography:Includes bibliographical references.
ISBN:9781461267690
1461267692
9781461204572
1461204577