Skip to main content

Unlikely Intersection and Uniform Bounds for Points

Project description

Uniform bounds on rational points of algebraic varieties under study

The EU-funded UnIntUniBd project aims to study the uniform bounds on rational and algebraic points. These include Mazur’s conjecture on the number of points on curves, which implies the following two strong bounds: the number of rational points on a smooth projective curve of genus g of at least 2 defined over a number field of degree d is bounded above in terms of g, d and the Mordell-Weil rank; and 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. The project also aims to generalise the first bound to higher-dimensional subvarieties of abelian varieties, and ultimately extend the bounds to semi-abelian varieties. As key techniques for the project, functional transcendence and unlikely intersection problems will also be investigated.

Call for proposal

ERC-2020-STG
See other projects for this call

Host institution

GOTTFRIED WILHELM LEIBNIZ UNIVERSITAET HANNOVER
Address
Welfengarten 1
30167 Hannover
Germany
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 364 063,50

Beneficiaries (2)

GOTTFRIED WILHELM LEIBNIZ UNIVERSITAET HANNOVER
Germany
EU contribution
€ 1 364 063,50
Address
Welfengarten 1
30167 Hannover
Activity type
Higher or Secondary Education Establishments
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS

Participation ended

France
EU contribution
€ 135 852,50
Address
Rue Michel Ange 3
75794 Paris
Activity type
Other