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 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 distinctive functions), investigated in a variety of elements. 3 classes research the most very important fresh principles within the optimistic attribute conception found by means of Goss (a box in tumultuous improvement, that is seeing a couple of surprising advances): they hide respectively crystals over functionality fields (with a few functions to L-functions of t-motives), gamma and zeta features in attribute p, and the binomial theorem. the opposite are fascinated about issues toward the classical conception of abelian kinds 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 concept explaining the hot 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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