Article contents
Fine Selmer groups of congruent p-adic Galois representations
Published online by Cambridge University Press: 29 September 2021
Abstract
We compare the Pontryagin duals of fine Selmer groups of two congruent p-adic Galois representations over admissible pro-p, p-adic Lie extensions
$K_\infty $
of number fields K. We prove that in several natural settings the
$\pi $
-primary submodules of the Pontryagin duals are pseudo-isomorphic over the Iwasawa algebra; if the coranks of the fine Selmer groups are not equal, then we can still prove inequalities between the
$\mu $
-invariants. In the special case of a
$\mathbb {Z}_p$
-extension
$K_\infty /K$
, we also compare the Iwasawa
$\lambda $
-invariants of the fine Selmer groups, even in situations where the
$\mu $
-invariants are nonzero. Finally, we prove similar results for certain abelian non-p-extensions.
Keywords
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- © Canadian Mathematical Society 2021
References
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