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arXiv · 1604.04571

Level structures on abelian varieties and Vojta's conjecture

Dan Abramovich·Keerthi Madapusi Pera·Anthony Várilly-Alvarado
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Abstract

Assuming Vojta's conjecture, and building on recent work of the authors, we prove that, for a fixed number field $K$ and positive integer $g$, there is an integer $m_0$ such that for any $m > m_0$ there is no principally polarized abelian variety $A/K$ of dimension $g$ with full level-$m$ structure. To this end, we develop a version of Vojta's conjecture for Deligne-Mumford stacks, which we deduce from Vojta's conjecture for schemes.

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Dan Abramovich, Keerthi Madapusi Pera, Anthony Várilly-Alvarado. 2016-04-15. Level structures on abelian varieties and Vojta's conjecture. https://doi.org/10.1112/s0010437x16008253

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