One says that a Diophantine equation satisfies the local-global principle if the existence of 'local' solutions modulo n for all integers n is enough to ensure the existence of 'global' solutions in the integers. This does not always hold, but when it does it provides a powerful tool for solving such equations. The aim of this project is to explore analogous local-global principles in the context of algebraic groups and identify situations in which they do and do not hold for the question of divisibility.

Does the project come with funding

No

Final date for receiving applications

Ongoing

Keywords

Number theory, algebra, geometry