AN APPLICATION OF LAZARD'S THEORY OF p-ADIC LIE GROUPS TO TORSION SELMER POINTED SETS

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.