132 , 2016-01 , Department of Mathematics, Faculty of Science, Okayama University
Let K be a real abelian field of odd degree over Q, and C the group of cyclotomic units of K. We denote by C+ and C0 the totally positive and primary elements of C, respectively. G. Gras found a duality between the Galois modules C+/C2 and C0/C2 by some ingenious calculation on cyclotomic units. We give an alternative proof using a consequence (=“Gras conjecture”) of the Iwasawa main conjecture and the standard reflection argument. We also give some related topics.