Generalized fine Selmer torsion conjecture over -adic Lie extensions
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.
Sources & referencesView supporting material
Primary source
Meng Fai Lim, “Structure of fine Selmer groups over Z_p-extensions”, arXiv:2111.08866 (2023).
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