Control Theorems for Fine Selmer Groups

作者：Kundu, Debanjana^*; Lim, Meng Fai

来源：Journal de Theorie des Nombres de Bordeaux, 2022, 34(3): 851-880.

DOI：10.5802/jtnb.1231

• ELLIPTIC-CURVES
• IWASAWA THEORY
• CONJECTURES
• EXTENSIONS
• FORMULA
• VALUES

We study the growth of the p-primary fine Selmer group, R(E/F ') , of an elliptic curve over an intermediate sub-extension F ' of a p-adic Lie extension, L/F. We estimate the Z(p)-corank of the kernel and cokernel of the restriction map r(L/F ') : R(E/F ')-> R(E /L)(Gal(L/F ')) with F ' a finite extension of F contained in L. We show that the growth of the fine Selmer groups in these intermediate sub-extension is related to the structure of the fine Selmer group over the infinite level. On specializing to certain (possibly non-commutative) p-adic Lie extensions, we prove finiteness of the kernel and cokernel and provide growth estimates on their orders.

• 单位
  6; 1