Abstract
Minhyong Kim defined the Selmer variety associated with a curve $X$ over a number field, which is a non-abelian analogue of the ${\mathbb Q}_p$-Selmer group of the Jacobian variety of $X$. In this paper, we define a torsion analogue of the Selmer variety. Recall that Mazur's control theorem describes the behavior of the torsion Selmer groups of an abelian variety with good ordinary reduction at $p$ in the cyclotomic tower of number fields. We give a non-abelian analogue of Mazur's control theorem by replacing the torsion Selmer group by a torsion analogue of the Selmer variety.
Citation
Kenji Sakugawa. "A control theorem for the torsion Selmer pointed set." Tohoku Math. J. (2) 70 (2) 175 - 223, 2018. https://doi.org/10.2748/tmj/1527904820