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

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 topic round which they're headquartered is the mathematics of L-functions (and different particular functions), investigated in a variety of features. 3 classes study probably the most vital fresh rules within the confident attribute conception came across via Goss (a box in tumultuous improvement, that is seeing a couple of miraculous advances): they disguise respectively crystals over functionality fields (with a couple of purposes to L-functions of t-motives), gamma and zeta services in attribute p, and the binomial theorem. the opposite are all in favour of issues toward the classical concept of abelian types 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 cutting-edge survey of Geometric Iwasawa thought explaining the new 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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