Advanced Courses in Mathematics - CRM Barcelona

Arithmetic Geometry over Global Function Fields

Authors: Böckle, G., Burns, D., Goss, D., Thakur, D., Trihan, F., Ulmer, D.

Editors: Bars, Francesc, Longhi, Ignazio, Trihan, Fabien (Eds.)

  • Includes a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell–Weil groups of high rank)
  • Provides an introduction to A-crystals, with applications to some of the central questions in the theory of L-functions in characteristic p
  • Features a discussion of Gamma, Zeta and Multizeta functions in characteristic p, from scratch to the boundary of current research
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eBook $39.99
price for USA (gross)
  • ISBN 978-3-0348-0853-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-0348-0852-1
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  • Online orders shipping within 2-3 days.
About this Textbook

This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell-Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings.

Table of contents (5 chapters)

  • Cohomological Theory of Crystals over Function Fields and Applications

    Böckle, Gebhard

    Pages 1-118

  • On Geometric Iwasawa Theory and Special Values of Zeta Functions

    Burns, David (et al.)

    Pages 119-181

  • The Ongoing Binomial Revolution

    Goss, David

    Pages 183-193

  • Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields

    Thakur, Dinesh S.

    Pages 195-279

  • Curves and Jacobians over Function Fields

    Ulmer, Douglas

    Pages 281-337

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-0348-0853-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-0348-0852-1
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
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Bibliographic Information

Bibliographic Information
Book Title
Arithmetic Geometry over Global Function Fields
Authors
Editors
  • Francesc Bars
  • Ignazio Longhi
  • Fabien Trihan
Series Title
Advanced Courses in Mathematics - CRM Barcelona
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0853-8
DOI
10.1007/978-3-0348-0853-8
Softcover ISBN
978-3-0348-0852-1
Series ISSN
2297-0304
Edition Number
1
Number of Pages
XIV, 337
Topics