"Relating Descent and codescent in Iwasawa theory"

Fix a p-adic Lie extension F_\infty/F. A classical feature of Iwasawa
theory is that one generally expects the ''arithmetic'' of F_\infty to
control that of the finite layers F_n. In this talk, I will examine the
following question: Given a sequence of Galois modules (A_n) endowed with
the structure of both a projective and inductive system (subject to a
normic compatibility), what can we hope to recover of the A_n's from the
associated Iwasawa modules (by projective and/or inductive limit)?