A generalization of the Contou-Carrère symbol

Abstract

[EN]Using techniques of Algebraic Geometry, the aim of this paper is to give a generalized definition of the Contou-Carrere symbol as a morphism of schemes. In fact, from formal schemes and Heisenberg groups, we provide a new definition of the Contou-Carrere symbol and a generalization of it associated with a separable extension k -> k(s). Moreover, a reciprocity law is proved and classical explicit reciprocity laws are recovered from it.