Tate Module of Rational Numbers and Picard Groups of the Integer Rings of theCyclic p-Groups

摘要

It is proved that the Tate module Tp(Q) of the field of rational numbers considered as an abelian group can be embedded into Pic(proj.lim Z(Cn)), where p is an odd prime number and Cn is the cyclic group of order pn. Coming back to a finite level the authors show that Pic(Z(C2)) is a direct sum of Galois groups of certain extensions of K1 = Q(zeta 1), where zeta 1 is a primitive p-root of unity.