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VOL. 63 | 2012 An abelian surface with constrained 3-power torsion
Christopher Rasmussen

Editor(s) Hiroaki Nakamura, Florian Pop, Leila Schneps, Akio Tamagawa

## Abstract

In my talk at the Galois Theoretic Arithmetic Geometry meeting, I described recent joint work with Akio Tamagawa on a finiteness conjecture regarding abelian varieties whose $\ell$-power torsion is constrained in a particular fashion. In the current article, we introduce the conjecture and provide some geometric motivation for the problem. We give some examples of the exceptional abelian varieties considered in the conjecture. Finally, we prove a new result—that the set $\mathscr{A}(\mathbb{Q},2,3)$ of $\mathbb{Q}$-isomorphism classes of dimension 2 abelian varieties with constrained 3-power torsion is non-empty, by demonstrating an explicit element of the set.

## Information

Published: 1 January 2012
First available in Project Euclid: 24 October 2018

zbMATH: 1321.14037
MathSciNet: MR3051251

Digital Object Identifier: 10.2969/aspm/06310449

Subjects:
Primary: 14H30
Secondary: 11G10, 11G32