Basic Notions: Ehud de Shalit (HUJI) " Hilbert's 12th problem - recent developments"

Thu, 16/05/201916:00-17:15
Ross 70
Hilbert's 12th problem (Kronecker's Jugendtraum) is one of the major open problems
in number theory. In its various forms it asks for an explicit construction of abelian extensions of a given number field F and related arithmetical ingredients such as units in these extensions, or an explicit description of their Galois group. The only fully developed cases are when F is the field of rational numbers (cyclotomy) or a quadratic imaginary field (complex multiplication). After a brief survey of these classical cases we shall describe some amazing developments, still largely conjectural, by Darmon and his collaborators (Dasgupta, Vonk) when F is a real quadratic field.