Riv. Mat. Univ. Parma, Vol. 7, No. 1, 2016

Evelina Viada[1]

Explicit height bounds and the effective Mordell-Lang Conjecture

Pages: 101-131
Received: 3 December 2015   
Accepted: 5 February 2016.
Mathematics Subject Classification (2010): Primary 11G50, 11G05, Secondary 14G05.
Keywords: Heights, Rational Points, Anomalous Intersections, Mordell-Lang Conjecture.
Author address:
[1] : Department of mathematics, ETH Zurich, Rämistrasse 101, CH-8092 Zurich, Swithzerland.

Abstract: We first give an overview of some landmark theorems and recent conjectures in Diophantine Geometry. In the elliptic case, we prove some new bounds for torsion anomalous points and we clarify the implications of several height bounds on the effective Mordell-Lang Conjecture. In addition, we explicitly bound the Néron-Tate height of the rational points of a new family of curves of increasing genus, proving the effective Mordell Conjecture for these curves.

Work supported by the FNS Fonds National Suisse

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