Circular units in the {Z}_p-extensions of real abelian fields of prime conductor

Abstract

The aim of this paper is to compute the cohomology groups of circular units in the \bi Z_p-extensions of a real abelian field of prime conductor. Even though the generators of circular units are described very complicatedly, their cohomology groups turn out to be as simple as one can expect compared to the cohomology groups of full unit group found by Iwasawa.