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Arithmetic Geometry over Global Function Fields (Paperback, 2014 ed.)
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Arithmetic Geometry over Global Function Fields (Paperback, 2014 ed.)
Series: Advanced Courses in Mathematics - CRM Barcelona
Expected to ship within 12 - 17 working days
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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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