FORMAL GROUPS AND THE NORM RESIDUE SYMBOL

Abstract

This paper investigates the canonical pairing associated with a one-dimensional formal group law over the ring of integers of a finite extension of and an isogeny , just as the Hilbert symbol is associated with the multiplicative law and the isogeny raising to the 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 -adic differentiation, the logarithm of the formal group law, the norm, and the trace. Bibliography: 8 titles.