English

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}
}
R2 v1 2026-06-28T06:13:55.480Z