Arithmetic geometry over global function fields: [electronic resource] /: by Gebhard Böckle, David Burns, David Goss, Dinesh Thakur, Fabien Trihan, Douglas Ulmer ; edited by Francesc Bars, Ignazio Longhi, Fabien Trihan.

Böckle, Gebhard,; Burns, David.,; Goss, David.,; Thakur, Dinesh; Trihan, Fabien.,; Ulmer, Douglas.,; Bars, Francesc.,; Longhi, Ignazio.,

doi:10.1007/978-3-0348-0853-8

Arithmetic geometry over global function fields [electronic resource] / by Gebhard Böckle, David Burns, David Goss, Dinesh Thakur, Fabien Trihan, Douglas Ulmer ; edited by Francesc Bars, Ignazio Longhi, Fabien Trihan.

Böckle, Gebhard, 1964-., author.; Burns, David., author.; Goss, David., author.; Thakur, Dinesh (Writer on public administration)., author.; Trihan, Fabien., author.; Ulmer, Douglas., author.; Bars, Francesc., editor.; Longhi, Ignazio., editor.; Trihan, Fabien., editor.

2014

QA241.5

Available Online

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Title

Arithmetic geometry over global function fields [electronic resource] / by Gebhard Böckle, David Burns, David Goss, Dinesh Thakur, Fabien Trihan, Douglas Ulmer ; edited by Francesc Bars, Ignazio Longhi, Fabien Trihan.

Author

Böckle, Gebhard, 1964-., author.

ISBN

9783034808538 electronic book
3034808534 electronic book
9783034808521

DOI

https://doi.org/10.1007/978-3-0348-0853-8

Published

Basel : Birkhäuser, 2014.

Language

English

Description

1 online resource (xiv, 337 pages).

Item Number

10.1007/978-3-0348-0853-8 doi

Call Number

QA241.5

Dewey Decimal Classification

512.7

Summary

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.

Bibliography, etc. Note

Includes bibliographical references.

Access Note

Access limited to authorized users.

Digital File Characteristics

text file PDF

Added Author

Burns, David., author.
Goss, David., author.
Thakur, Dinesh (Writer on public administration)., author.
Trihan, Fabien., author.
Ulmer, Douglas., author.
Bars, Francesc., editor.
Longhi, Ignazio., editor.
Trihan, Fabien., editor.

Series

Advanced courses in mathematics, CRM Barcelona. 2297-0304

Available in Other Form

Print version: 9783034808521