Hilbert's 12th problem via p-adic Galois deformationsMPIM

by Michael Daas (Universität Luxemburg)

Thursday Jul 23, 2026, 3:00 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

MPI-Oberseminar

Class field theory describes the structure of all abelian field extensions of a number field, and promises the existence of the so-called Hilbert class field.
However, its explicit construction has been a long standing open problem, and doing this with the special values of arithmetic functions is known as Hilbert's 12th problem.
We discuss some cases in which this problem has been solved, including imaginary quadratic fields through CM theory and singular moduli.
Finally, we introduce novel p-adic constructions and outline a method to compute these special values using the p-adic infinitesimal deformation theory of Eisenstein series and theta series.