A Contou-Carrère symbol on Gl(n,A((t))) and a Witt residue theorem on Mat(n,ΣC)

In order to obtain a unified theory of one-dimensional symbols, the aim of this work is to give a definition of the Contou-Carrère symbol over the linear group Gl(n,A((t))) and to construct from it a generalization of the Witt residue to the group Mat(n,k((t))). Moreover, we offer a reciprocity law for the symbol when C is a complete algebraic curve and we deduce a Witt residue theorem on Mat(n,ΣC) as a particular case of this new reciprocity law.