On the tame symbol of an algebraic curve

Abstract

[EN]The aim of this work is to give a new definition of the tame symbol of an algebraic curve from the commutator of a certain central extension of groups. The definition offered is valid for each closed point p 2 C of an irreducible non singular curve over a perfect field. Moreover, when the curve is complete, the reciprocity law can be deduced from the finiteness of the cohomology groups H^0 (C, O_C) and H^1 (C, O_C).