Tohoku Mathematical Journal

A control theorem for the torsion Selmer pointed set

Kenji Sakugawa

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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.

Article information

Source
Tohoku Math. J. (2), Volume 70, Number 2 (2018), 175-223.

Dates
First available in Project Euclid: 2 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1527904820

Digital Object Identifier
doi:10.2748/tmj/1527904820

Mathematical Reviews number (MathSciNet)
MR3810239

Zentralblatt MATH identifier
06929333

Subjects
Primary: 11R23: Iwasawa theory
Secondary: 11R34: Galois cohomology [See also 12Gxx, 19A31]

Keywords
Selmer variety control theorem Iwasawa theory

Citation

Sakugawa, Kenji. A control theorem for the torsion Selmer pointed set. Tohoku Math. J. (2) 70 (2018), no. 2, 175--223. doi:10.2748/tmj/1527904820. https://projecteuclid.org/euclid.tmj/1527904820


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