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arXiv · 2211.10368

The norm residue symbol for formal Drinfeld modules

Marwa Ala Eddine·Behzad Omidi Koma
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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.

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Marwa Ala Eddine, Behzad Omidi Koma. 2022-11-18. The norm residue symbol for formal Drinfeld modules. https://arxiv.org/abs/2211.10368

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