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UID:7917@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20160125T140000
DTEND;TZID=Europe/Paris:20160125T150000
DTSTAMP:20241120T205605Z
URL:https://www.i2m.univ-amu.fr/evenements/uniformity-results-in-diophanti
 ne-geometry/
SUMMARY:Amos Turchet (...): Uniformity Results in Diophantine Geometry
DESCRIPTION:Amos Turchet: In 1997 Caporaso\, Harris and Mazur proved that L
 ang Conjecture (i.e. rational points in general type varieties are not Zar
 iski dense) implies that the number of rational point in curves of genus &
 gt\; 1 are not only finite (Falting’s Theorem) but uniform\; in particul
 ar there exists a bound for their number depending only on the genus and o
 n the base field. This result has been extended to surfaces of general typ
 e by work of Hassett. Analogous problems have been treated for (stably) in
 tegral points - introduced by Abramovich - for elliptic curves and princip
 ally polarised abelian varieties\, where uniformity\, conditionally on Lan
 g-Volta Conjecture\, has been proved to hold by work of Abramovich and Abr
 amovich-Matzuki. The focus of the talk will be an introduction to the subj
 ects and its links with questions of positivity of bundles and the theory 
 of stable pairs. If time permits I will report on a work-in-progress proje
 ct\, joint with Kenneth Ascher\, aiming to extend the results for integral
  points to all log general type surfaces.\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Amos_Turchet.jpg
CATEGORIES:Séminaire,Dynamique et Topologie
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