Meng Fai Lim
Published 2013-06-09, updated 2015-06-17Version 2
In this paper, we study the fine Selmer groups 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 $\Zp$-extension is intimately related to the variation of the class groups in the cyclotomic tower. We also discuss some examples of pseudo-nullity of fine Selmer groups.
Comments: 31 pages, numerous corrections and changes
Field change for the Cassels-Tate pairing and applications to class groups
The index of Rubin-Stark units
On $p$-class groups of relative cyclic $p$-extensions
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