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UnIntUniBd

Financiado
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) t... 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 existing results, the Faltings height is no longer involved in the bounds. The proofs I propose are via Diophantine estimates. Functional transcendence and unlikely intersections on mixed Shimura varieties play important roles in the proofs. Hence as pre-requests and extensions of the three goals listed above, I will also continue investigating on functional transcendence and unlikely intersection theories as well as their potential other interesting applications in Diophantine geometry. ver más
31/08/2025
LUH
1M€
Duración del proyecto: 60 meses Fecha Inicio: 2020-08-20
Fecha Fin: 2025-08-31

Línea de financiación: concedida

El organismo H2020 notifico la concesión del proyecto el día 2020-08-20
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
ERC-2020-STG: ERC STARTING GRANTS
Cerrada hace 5 años
Presupuesto El presupuesto total del proyecto asciende a 1M€
Líder del proyecto
GOTTFRIED WILHELM LEIBNIZ UNIVERSITAET HANNOV... No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5