ERC Starting Grant · 2020
Unlikely Intersection and Uniform Bounds for Points
I propose to investigate the following long expected but widely open uniform bounds on rational and algebraic points. (1) Mazur’s conjecture on the number of points on curves, which implies the following two strong bounds: (1.i) the number of rational points on a smooth projective curve of genus g at least 2 defined over a number field of degree d is bounded above in terms of g, d and the Mordell- Weil rank; (1.ii) the number of algebraic torsion points on a smooth projective curve of genus g at least 2 is bounded above only in terms of g. (2) Generalize the bound in (1) to higher dimensional subvarieties of abelian varieties. (3) Extend the bounds to semi-abelian varieties. Compared with…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.