# A note on the Manin-Mumford conjecture

Source: [A note on the Manin-Mumford conjecture](<https://www.sota2.com/research/paper/68fa50f81e209131ce96fc1b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T11:09:30.716Z

Authors: K. Chen

Published: 2014-05-23T13:04:58.000Z

## Abstract

In this paper we prove a special case of the Andr\\'e-Oort conjecture for Kuga varieties. If $M$ is a Kuga variety fibred over a pure Shimura variety $S$ as an abelian scheme, and $(M\_n)$ is a sequence of special subvarieties in $M$ which are faithfully flat over $S$, then the Zariski closure of the union of the $M\_n$'s is a finite union of special subvarieties faithfully flat over $S$. The proof is reduced to a variant of the Manin-Mumford conjecture for abelian schemes.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1405.6053>)

[PDF](<https://arxiv.org/pdf/1405.6053.pdf>)