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 worldwide fields; the typical subject round which they're founded is the mathematics of L-functions (and different specific functions), investigated in a variety of facets. 3 classes research the most vital contemporary rules within the optimistic attribute concept came across through Goss (a box in tumultuous improvement, that's seeing a couple of dazzling advances): they hide respectively crystals over functionality fields (with a few functions to L-functions of t-motives), gamma and zeta services in attribute p, and the binomial theorem. the opposite are taken with issues towards the classical idea of abelian kinds over quantity fields: they provide 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 cutting-edge survey of Geometric Iwasawa idea explaining the new proofs of assorted types of the most Conjecture, within the commutative and non-commutative settings.
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