The well-known Kronecker-Weber theorem affirms that every finite abelian extension of the field ℚ of rational numbers belongs to some cyclotomic extension ℚ(t|tn=1). In his 12th problem D.Hilbert asked how to generalize this theorem for other global fields. In this talk, we give the exposition of the actual state of this problem together with the connection with Carlitz-Drinfeld-Anderson modules. Recall that Anderson module M is a (left) module over non-commutative ring R=Cp[T,τ], Tτ=τT, τa=ap τ, where Cp is a some field of characteristic p greater than 0, such that M is free finite generated over subrings Cp[T] and Cp[τ].
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
