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 à 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 Anglès 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.