Arithmetic Geometry over Global Function Fields (Advanced - download pdf or read online

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 study Programme 2009-2010 on the CRM Barcelona. them all take care of attribute p worldwide fields; the typical topic round which they're established is the mathematics of L-functions (and different precise functions), investigated in a variety of features. 3 classes study essentially the most vital contemporary principles within the optimistic attribute conception chanced on by way 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 functions to L-functions of t-motives), gamma and zeta features in attribute p, and the binomial theorem. the opposite are interested in issues towards the classical concept of abelian kinds over quantity fields: they provide 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 conception explaining the hot proofs of assorted models of the most Conjecture, within the commutative and non-commutative settings.

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Arithmetic Geometry over Global Function Fields (Advanced Courses in Mathematics - CRM Barcelona) by Gebhard Böckle,David Burns,David Goss,Dinesh Thakur,Fabien Trihan,Douglas Ulmer,Francesc Bars,Ignazio Longhi


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