Algebraic Curves, Adeles and Weil Reciprocity Law

Francisco J. Plaza-Martín
(A joint work with Luis M. Navas, José M. Muñoz and Fernando Pablos)
Universidad de Salamanca
Abstract:
In this talk we will apply ideas of Class Field Theory to the study of the function field of an algebraic curve defined over a perfect base field. More precisely, we will consider a subgroup of the idele class group and, using the Weil Reciprocity Law and the theory of topological groups, we will show how this subgroup encodes arithmetic and geometric properties of the curve. Finally, these results will allow us to deduce results on the coverings of the curve.