摘要

In this paper, we study the fine Selmer group attached to a Galois module defined over a commutative complete Noetherian ring with finite residue field of characteristic p. Namely, we are interested in its properties upon taking residual representation and within field extensions. In particular, we will show that the variation of the fine Selmer group in a cyclotomic Z(p)-extension is intimately related to the variation of the class groups in the cyclotomic tower.