PERIODIC FUNCTIONS, TOROIDAL GROUPS, GENERALIZED JACOBIANS, AND FRACTIONAL IDEALS OF NON-TOTALLY REAL NUMBER FIELDS

Abstract

In this paper, we collect a series of results exposed by the second author in Batumi on the occasion of XIV Annual International Conference of the Georgian Mathematical Union. These results connect the beautiful theory of toroidal groups and non-totally real number fields with that of generalized Jacobians of hyperelliptic curves.