The norm residue symbol for formal Drinfeld modules

Abstract: In this paper, we study the Kummer pairing associated with formal Drinfeld modules having stable reduction of height one. We give an explicit description of the pairing `a la Kolyvagin, in terms of the logarithm of the formal Drinfeld module, a certain derivation, torsion points and the trace. The results obtained give a generalization of the results of Angl`es proved for Carlitz modules, and of Bars and Longhi proved for sign-normalized rank one Drinfeld modules. It also presents an extension of our previous formulas to arbitrary finite extensions of loca fields containing enough torsion points.