Geodesic
Fine Selmer groups of congruent p-adic Galois representations
Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 702-722

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DOI

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.
DOI : 10.4153/S0008439521000849
Mots-clés : Admissible p-adic Lie extension, abelian variety, p-adic Galois representation, fine Selmer group, Iwasawa invariants 
Kleine, Sören; Müller, Katharina. Fine Selmer groups of congruent p-adic Galois representations. Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 702-722. doi: 10.4153/S0008439521000849
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     author = {Kleine, S\"oren and M\"uller, Katharina},
     title = {Fine {Selmer} groups of congruent p-adic {Galois} representations},
     journal = {Canadian mathematical bulletin},
     pages = {702--722},
     year = {2022},
     volume = {65},
     number = {3},
     doi = {10.4153/S0008439521000849},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000849/}
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