The growth of fine Selmer groups

Abstract

Let A be an abelian variety defined over anumber field F. In this paper, we will investigate the growth of p-rank of the fine Selmer group in three situations. In particular, in each of these situations, we show that there is a strong analogy between the growth of the p-rank of the fine Selmer group and the growth of the p-rank of the class groups.

16 pages, some minor corrections and changes

References in corpus (1)

• Selmer groups of elliptic curves in degree $p$ extensions

Cited by in corpus (7)

• Fine Selmer groups of congruent Galois representations
• On fine Selmer groups and signed Selmer groups of elliptic modular forms
• Fine Selmer groups of congruent $p$-adic Galois representations
• Fine Selmer groups and ideal class groups
• Anticyclotomic $\mu$-invariants of residually reducible Galois Representations
• On the control theorem for fine Selmer groups and the growth of fine Tate-Shafarevich groups in ${\mathbb{Z}}_p$-extensions
• On pseudo-nullity of fine Mordell-Weil group