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

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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 situated is the mathematics of L-functions (and different distinctive functions), investigated in numerous facets. 3 classes learn probably the most very important fresh rules within the optimistic attribute idea found through Goss (a box in tumultuous improvement, that is seeing a few mind-blowing advances): they disguise respectively crystals over functionality fields (with a few purposes to L-functions of t-motives), gamma and zeta services in attribute p, and the binomial theorem. the opposite are interested in issues in the direction of the classical concept of abelian types over quantity fields: they offer respectively an intensive creation 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 state-of-the-art survey of Geometric Iwasawa thought explaining the new proofs of varied 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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