CRM: Centro De Giorgi
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Third Italian Number Theory Meeting

Uniformity results in Diophantine Geometry

speaker: Amos Turchet (Chalmers University of Technology)

abstract: In 1997 Caporaso, Harris and Mazur proved that Lang Conjecture (i.e. rational points in general type varieties are not Zariski dense) implies that the number of rational point in curves of genus > 1 are not only finite (Falting’s Theorem) but uniform; in particular there exists a bound for their number depending only on the genus and on the base field. This result has been extended in higher dimension by Hassett and Abramovich-Voloch. Analogous problems have been treated for (stably) integral points - introduced by Abramovich - for elliptic curves and principally polarised abelian varieties by work of Abramovich and Abramovich-Matzuki. I will report on a work-in-progress project, joint with Kenneth Ascher, aiming to extend the results for integral points to all log general type surfaces.

Wed 23 Sep, 16:30 - 16:55, Aula Russo
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