Explicit reciprocity laws for formal Drinfeld modules

par - publié le

Jeudi 23 juin 2022
Marwa alaeddine
(Université de Franche-Comté)

Explicit reciprocity laws for formal Drinfeld modules

We prove explicit reciprocity laws for a class of formal Drinfeld modules having stable reduction of height one, in the spirit of those existing in characteristic zero. We begin by defining the Kummer pairing in the language of formal Drinfeld modules defined over local fields of positive characteristic. We then prove explicit formulas for this pairing in terms of the logarithm of the formal Drinfeld module, a certain Coleman power series, torsion points and the trace.