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Arithmetic Geometry over Global Function Fields (Advanced Courses in Mathematics - CRM Barcelona)

De (autor) , , , , , Editat de Francesc Bars, Ignazio Longhi
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en Limba Engleză Carte Paperback – 04 Dec 2014
Arithmetic Geometry over Global Function Fields
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Din seria Advanced Courses in Mathematics - CRM Barcelona

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Specificații

ISBN-13: 9783034808521
ISBN-10: 3034808526
Pagini: 341
Ilustrații: Bibliographie
Dimensiuni: 168 x 240 x 17 mm
Greutate: 0.67 kg
Ediția: 2014
Editura: Springer
Colecția Birkhäuser
Seria Advanced Courses in Mathematics - CRM Barcelona

Locul publicării: Basel, Switzerland

Public țintă

Graduate

Textul de pe ultima copertă

This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009–2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell–Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings.

Caracteristici

Includes a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell–Weil groups of high rank)
Provides an introduction to A-crystals, with applications to some of the central questions in the theory of L-functions in characteristic p
Features a discussion of Gamma, Zeta and Multizeta functions in characteristic p, from scratch to the boundary of current research