Local-global principles for divisibility in algebraic groups

Host Faculty: Engineering
General Subject Area: Pure Mathematics
Project Level: PhD
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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.


Supervisor: Brendan Creutz

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Number theory, algebra, geometry