Arithmetic Geometry over Global Function Fields

Arithmetic Geometry over Global Function Fields

Description

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.


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Details

Author(s)
Gebhard Bockle, Dr. David Burns, David Goss, Dinesh S. Thakur, Fabien Trihan, Douglas Ulmer, Francesc Bars, Ignazio Longhi
Format
Paperback | 337 pages
Dimensions
168 x 240 x 14.73mm | 671.32g
Publication date
01 Jan 2015
Publisher
Springer Basel
Publication City/Country
Switzerland
Language
English
Edition Statement
2014 ed.
Illustrations note
XIV, 337 p.
ISBN10
3034808526
ISBN13
9783034808521