Noncommutative torsion conjecture for Selmer groups over strongly admissible extensions

Let F/FF_\infty/F be a strongly admissible pp-adic Lie extension: it is Galois, contains the cyclotomic Zp\mathbb{Z}_p-extension, is unramified outside finitely many primes, and Gal(F/F)\operatorname{Gal}(F_\infty/F) has no pp-torsion. Write G=Gal(F/F)G=\operatorname{Gal}(F_\infty/F) and let X(E/F)X(E/F_\infty) be the Pontryagin dual of the Selmer group. Noncommutative torsion conjecture. The module X(E/F)X(E/F_\infty) is torsion over Zp[[G]]\mathbb{Z}_p[[G]]. This is the natural extension of the cyclotomic torsion conjecture to pp-adic Lie extensions; the source gives no resolution status.

Sources & referencesView supporting material

Primary source

Meng Fai Lim, “On order of vanishing of characteristic elements”, arXiv:2109.03985 (2022).

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