CORDIS Project
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This project focuses on establishing uniform bounds for rational and algebraic points on curves and higher-dimensional varieties. It aims to advance mathematical understanding through Diophantine estimates and explore their implications in Diophantine geometry.
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…
GOTTFRIED WILHELM LEIBNIZ UNIVERSITAET HANNOVER
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