May 12 (Wednesday) 2021 16:00 - 18:00, Building 110, Room N103
Speaker : Jinjoo Yoo (UNIST)
Title : Class groups of cyclic function fields over the rational function field
Abstract : An algebraic function field is an algebraic extension of finite degree over the rational function field. This field extension occurs in various branches of mathematics such as algebraic geometry, number theory, and compact Riemann surfaces. In the first half of this talk, I will give a brief overview of the general theory of algebraic function fields, including basic concepts, class groups, and Galois extensions of function fields. For the second half, I will focus on cyclic extensions over the rational function field and discuss the structures of class groups of such field extensions.