... to H1(Q,W()f) are called ordinary at . (In [Ram, §3], these classes are referred to as null cocycles.)Note that H1(Q,Wf) decomposes as a direct sum of two one-dimensionalFp-subspaces,H1(Q,Wf)=H1fin(Q,Wf)⊕H1ord(Q,W()f),whereH1fin(Q,Wf):=H1(Qnr/Q,Wf)is ... SelS(Q,Wf) consisting of classes that are trivial at the primes in S.This notation can be combined: thus, if S1,S2,S3 are pairwise coprime square-free products of admissible primes, ... that forn<∞, the modules Af,nand Tf,n are isomorphic as GQ-modules, but the Af,nfit naturally into an inductive system while the Tf,n are part of a projectivesystem. It is therefore...