2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112647In this note we will study the Hilbert 12th problem for a primitive CM field, and the corresponding Stark conjectures. Using the idea of Mirror Symmetry, we will show how to generate all the class fields of a given primitive CM field, thus complete the work of Shimura- Taniyama-Weil.Research Notes. Draft version. Feedback welcomeNumber TheoryAlgebraic Geometrytext