Read e-book online Arithmetic Geometry over Global Function Fields (Advanced PDF

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

ISBN-10: 3034808526

ISBN-13: 9783034808521

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 worldwide fields; the typical subject round which they're founded is the mathematics of L-functions (and different unique functions), investigated in quite a few facets. 3 classes learn essentially the most vital fresh rules within the optimistic attribute thought came across through Goss (a box in tumultuous improvement, that is seeing a few astounding 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 inquisitive about issues towards the classical idea of abelian forms over quantity fields: they provide respectively a radical 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 conception explaining the hot proofs of assorted 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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