Abstract
We construct torsion Selmer pointed sets, which are a discrete analogue of Selmer schemes. Such torsion objects were first defined by K. Sakugawa under a hypothesis, who also established a control theorem for them. We remove the hypothesis and provide the discrete analogue in full generality, to which Sakugawa's control theorem extends as well. As a key ingredient, we use Lazard's theory to build the unipotent completion of a finitely generated group over $p$-adic integers.
Acknowledgments
The author is grateful to an anonymous referee for pointing out and correcting an error and providing helpful comments. This work was supported by the National Research Foundation of Korea and Samsung Science and Technology Foundation.
Citation
Dohyeong Kim. "An application of Lazard's theory of $p$-adic Lie groups to torsion Selmer pointed sets." Osaka J. Math. 60 (3) 701 - 708, July 2023.
Information