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

This quantity collects the texts of 5 classes given within the mathematics Geometry examine Programme 2009-2010 on the CRM Barcelona. them all take care of attribute p international fields; the typical topic round which they're situated is the mathematics of L-functions (and different designated functions), investigated in a number of facets. 3 classes study the most very important fresh principles within the optimistic attribute concept stumbled on via Goss (a box in tumultuous improvement, that's seeing a few outstanding advances): they conceal respectively crystals over functionality fields (with a couple of purposes to L-functions of t-motives), gamma and zeta capabilities in attribute p, and the binomial theorem. the opposite are keen on subject matters towards the classical idea 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 conception explaining the new 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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