Geodesic
Formal groups and the norm residue symbol
Izvestiya. Mathematics , Tome 15 (1980) no. 2, pp. 289-348

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This paper investigates the canonical pairing associated with a one-dimensional formal group law $F$ over the ring of integers of a finite extension of $\mathbf Q_p$ and an isogeny $f\colon F\to F$, just as the Hilbert symbol is associated with the multiplicative law and the isogeny "raising to the $p$th power". Formulas are obtained which generalize the formulas of Artin–Hasse, Iwasawa, and Wiles. The formulas describe the values of the symbol in terms of $p$-adic differentiation, the logarithm of the formal group law, the norm, and the trace. Bibliography: 8 titles. 
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     author = {V. A. Kolyvagin},
     title = {Formal groups and the norm residue symbol},
     journal = {Izvestiya. Mathematics },
     pages = {289--348},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {1980},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1980_15_2_a4/}
}
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V. A. Kolyvagin. Formal groups and the norm residue symbol. Izvestiya. Mathematics , Tome 15 (1980) no. 2, pp. 289-348. http://geodesic.mathdoc.fr/item/IM2_1980_15_2_a4/