The norm residue symbol for formal Drinfeld modules
Number Theory
2022-11-21 v1
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.
Keywords
Cite
@article{arxiv.2211.10368,
title = {The norm residue symbol for formal Drinfeld modules},
author = {Marwa Ala Eddine},
journal= {arXiv preprint arXiv:2211.10368},
year = {2022}
}