Adelic and idelic pairings related to Weil reciprocity on algebraic curves

Abstract

[EN] In this paper we present an overview of some recent results con cerning the properties of a function field embedded in the adeles. Specifically, for an algebraic curve over a perfect field, Weil reciprocity allows us to define a subgroup of the idele class group whose topology encodes arithmetic prop erties of the base field and geometric properties of the curve. In particular we establish a relationship with the Picard group. The construction is inspired by Tate’s results on the character group of the adeles over a global field.