Arithmetic Geometry over Global Function Fields (Advanced by Gebhard Böckle,David Burns,David Goss,Dinesh Thakur,Fabien

By Gebhard Böckle,David Burns,David Goss,Dinesh Thakur,Fabien Trihan,Douglas Ulmer,Francesc Bars,Ignazio Longhi

This quantity collects the texts of 5 classes given within the mathematics Geometry examine Programme 2009-2010 on the CRM Barcelona. them all care for attribute p international fields; the typical subject matter round which they're established is the mathematics of L-functions (and different precise functions), investigated in quite a few points. 3 classes research essentially the most vital fresh principles within the confident attribute conception found by means of Goss (a box in tumultuous improvement, that's seeing a few unbelievable advances): they conceal respectively crystals over functionality fields (with a couple of purposes to L-functions of t-motives), gamma and zeta features in attribute p, and the binomial theorem. the opposite are concerned with themes towards the classical conception of abelian kinds over quantity fields: they offer respectively an intensive advent to the mathematics of Jacobians over functionality fields (including the present prestige of the BSD conjecture and its geometric analogues, and the development of Mordell-Weil teams of excessive rank) and a cutting-edge survey of Geometric Iwasawa idea explaining the new proofs of varied types of the most Conjecture, within the commutative and non-commutative settings.

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