Download e-book for kindle: Arithmetic Geometry over Global Function Fields (Advanced by Gebhard Böckle,David Burns,David Goss,Dinesh Thakur,Fabien

Download e-book for kindle: 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 study Programme 2009-2010 on the CRM Barcelona. them all take care of attribute p international fields; the typical subject matter round which they're headquartered is the mathematics of L-functions (and different precise functions), investigated in quite a few features. 3 classes learn probably the most vital fresh principles within the optimistic attribute concept stumbled on through Goss (a box in tumultuous improvement, that's seeing a couple of extraordinary advances): they hide 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 all for subject matters towards the classical thought of abelian types 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 idea explaining the hot proofs of varied types 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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