The geometric torsion conjecture for abelian varieties with real multiplication

@article{Bakker2015TheGT,
title={The geometric torsion conjecture for abelian varieties with real multiplication},
author={Benjamin Bakker and Jacob Tsimerman},
journal={arXiv: Algebraic Geometry},
year={2015}
}

The geometric torsion conjecture asserts that the torsion part of the Mordell--Weil group of a family of abelian varieties over a complex quasiprojective curve is uniformly bounded in terms of the genus of the curve. We prove the conjecture for abelian varieties with real multiplication, uniformly in the field of multiplication. Fixing the field, we furthermore show that the torsion is bounded in terms of the $\mathit{gonality}$ of the base curve, which is the closer analog of the arithmetic… CONTINUE READING