On a generalization of Tate dualities with application to Iwasawa theory

Abstract

this paper. Let l; p be two primes of Q. Let K=Q be a finite Galois extension, G = Gal(K=Q). Let GK = Gal(K=K). For a prime v over l, let K v be the completion of K at v and let GKv = Gal(K v =K v ). For any p-primary abelian group M , denote M n for kerfp n : M ! Mg unless defined otherwise. M div is used to denote its maximal divisible subgroup, and M cot