An n-dimensional Contou–Carrère symbol over an artinian local ring

Abstract

[EN]The aim of this work is to give a definition of an n-dimensional Contou–Carrère symbol. This symbol allows us to define an n-dimensionalWitt residue. Moreover, we offer a reciprocity law for the symbol related to a flag of irreducible varieties, in order to obtain an n-dimensional Witt residue Theorem as a particular case of this new reciprocity law.