Download e-book for iPad: 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 round which they're established is the mathematics of L-functions (and different unique functions), investigated in numerous features. 3 classes research essentially the most very important contemporary principles within the confident attribute concept came upon through Goss (a box in tumultuous improvement, that's seeing a few astonishing advances): they disguise respectively crystals over functionality fields (with a few purposes to L-functions of t-motives), gamma and zeta features in attribute p, and the binomial theorem. the opposite are involved in themes towards the classical thought of abelian types over quantity fields: they provide respectively a radical 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 thought 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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