Explicit formulas for the Kurihara's homomorphism
by
V. G. Boitsov
St.-Petersburg University, Department of Mathematics and Mechanics
Coauthors: Prof. I. B. Zhukov

Let K be a henselian discrete valuation field with residue field F. If F is finite, local class field theory gives the precise knowledge concerning the abelian extentions of K. In paper of Masato Kurihara: Abelian extentions of an absolutely unramified local field with general residue field, Invent. math., 93(1988). 451-480 with assumption that an odd prime p is a pime element of the integer ring of K given a new tool wich determines the feature of abelian extentions of K by analyzing groups H¹(K, Z/pⁿ)=Hom(Gal(K^sep/K), Z/pⁿ). For this purpose proved the existense of homomorphism

\Phin:H1(K, Z/pn) --> Wn(F)

where W_n(F) the ring of Witt vectors of length n over F. In this work we give an explicit formulas for this homomorphism.

Date received: November 2, 2000