In This Paper We Construct a Pairingon the Group of Degree Zero Divisors of a Curve Over a Number Field. This Isaccomplished By Passing from Divisors of the Curve to Divisors of an Associatedscheme and Then Employing an Arakelov Intersection Theory. Arakelov Geometrystudies a Scheme X Over the Ring of Integers Z, By Putting Hermitian Metrics Onholomorphic Vector Bundles Over X(C), the Complex Points of X. This Extrahermitian Structure Is Applied As a Substitute, For the Failure of the Schemespec(Z) to Be a Complete Variety..