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Bounds for the number of rational points on curves over global fields
Post-edited
Authors : Pazuki, Fabien (Author of the conference)
CIRM (Publisher )
11G35 - Varieties over global fields
14G05 - Rational points
CIRM (Publisher )
Abstract :
Rational points on smooth projective curves of genus $g \ge 2$ over number fields are in finite number thanks to a theorem of Faltings from 1983. The same result was known over function fields of positive characteristic since 1966 thanks to a theorem of Samuel. The aim of the talk is to give a bound as uniform as possible on this number for curves defined over such fields. In a first part we will report on a result by Rémond concerning the number field case and on a way to strengthen it assuming a height conjecture. During the second part we will focus on function fields of positive characteristic and describe a new result obtained in a joined work with Pacheco.
MSC Codes : 11G35 - Varieties over global fields
14G05 - Rational points
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English;French Available date : 28/04/14 Conference Date : 12/03/2014 Subseries : Research talks arXiv category : Number Theory ; Algebraic Geometry Mathematical Area(s) : Algebra ; Number Theory Format : QuickTime (.mov) Video Time : 00:53:57 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2014-03-12_Pazuki.mp4 
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Information on the Event
Event Title : Number theory and applications / Théorie des nombres et applicationsEvent Organizers : Maire, Christian ; Ricotta, Guillaume Dates : 10/03/14 - 14/03/14 Event Year : 2014
Citation Data
DOI : 10.24350/CIRM.V.18477603Cite this video as: Pazuki, Fabien (2014). Bounds for the number of rational points on curves over global fields. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18477603 URI : http://dx.doi.org/10.24350/CIRM.V.18477603 |
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