2022/11/18 by Marwa Eddine, Eddine, Marwa Ala, Koma, Behzad Omidi
Mathematics · #11F85 #11S31 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2211.10368
openalex publication_date 2022/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.