Progress in Mathematics

Arithmetic Algebraic Geometry

Editors: Geer, G., van der, Oort, F., Steenbrink, Joseph (Eds.)

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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.

Table of contents (20 chapters)

Table of contents (20 chapters)

Buy this book

eBook 93,08 €
price for Spain (gross)
  • ISBN 978-1-4612-0457-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 145,59 €
price for Spain (gross)
  • ISBN 978-0-8176-3513-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 114,39 €
price for Spain (gross)
  • ISBN 978-1-4612-6769-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Arithmetic Algebraic Geometry
Editors
  • G., van der Geer
  • F. Oort
  • Joseph Steenbrink
Series Title
Progress in Mathematics
Series Volume
89
Copyright
1991
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0457-2
DOI
10.1007/978-1-4612-0457-2
Hardcover ISBN
978-0-8176-3513-8
Softcover ISBN
978-1-4612-6769-0
Series ISSN
0743-1643
Edition Number
1
Number of Pages
X, 444
Topics