Generalized fine Selmer torsion conjecture over -adic Lie extensions
Let be one of the coefficient objects considered in the source, with coefficient ring , and let be a -adic Lie extension such that is pro-, has no -torsion, and is unramified outside a finite set of primes. Let be the Pontryagin dual of the corresponding fine Selmer group. Generalized fine Selmer torsion conjecture. For every such -adic Lie extension,
This extends the -extension torsion conjectures to noncommutative -adic Lie extensions and is motivated by known torsion results for related étale wild kernels. The generalized assertion remains open in the stated generality.
References
Primary source
Meng Fai Lim, “Structure of fine Selmer groups over Z_p-extensions”, arXiv:2111.08866 (2023).
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