Tohoku Mathematical Journal
2018
June
SECOND SERIES VOL. 70, NO. 2

Tohoku Math. J.
70 (2018), 175-223

Title A CONTROL THEOREM FOR THE TORSION SELMER POINTED SET

Author Kenji Sakugawa

(Received December 3, 2012, revised December 9, 2015)
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.

Mathematics Subject Classification. Primary 11R23; Secondary 11R34.
Key words and phrases. Selmer variety, control theorem, Iwasawa theory.

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