An Explicit Formula for the Picard Group of the Cyclic Group of Order p 2

On the Picard Group of the Integer Group Ring of the Cyclic p-Group and Certain Galois Groups

“…The diagrams above show that the proj.limit(Pic Z[C n ])$ proj.limit(Pic A n ). Therefore, it suffices to prove (1) and (2). Let us first prove (1).…”

“…The structure of the group B 2 was established for all odd p in [2]. Using the norm maps we can obtain some information about the structure of B n for n>2.…”

“…In this section we will discuss a connection between Galois groups and Pic Z[C 2 ], which is computed explicitly in [2] in terms of class groups of cyclotomic fields Q(`i) for i=1, 2.…”

“…K Last Remark. If p is a properly irregular prime then we can view the explicit formula for Pic Z[C 2 ] obtained in [2] as an explicit formula for Gal(M(0, p&1)ÂK 1 ) (in the notations of this paper). In particular this means that …”

Vandiver's Conjecture via K-theory

“…1.1 Review of necessary results of [5] Let us consider the Picard group of the integer group ring ZC 2 . The first observation is that P ic(ZC 2 ) ∼ = P ic(A), where A can be presented as a Cartesian product of Z[ Here P ic, the Picard group, is the same as the projective class group or simply the class group for Dedekind rings.…”