The Oort conjecture on Shimura curves in the Torelli locus of hyperelliptic curves

Xin Lu; Kang Zuo

doi:10.1016/j.matpur.2017.05.002

The Oort conjecture on Shimura curves in the Torelli locus of hyperelliptic curves

Xin Lu^*
, Kang Zuo

^*此作品的通讯作者

Johannes Gutenberg University Mainz

科研成果: 期刊稿件 › 文章 › 同行评审

14 引用（Scopus）

摘要

Oort has conjectured that there do not exist Shimura varieties of dimension >0 contained generically in the Torelli locus of genus-g curves when g is sufficiently large. In this paper we prove the analogue of this conjecture for Shimura curves with respect to the hyperelliptic Torelli locus of genus g>7.

源语言	英语
页（从-至）	532-552
页数	21
期刊	Journal des Mathematiques Pures et Appliquees
卷	108
期	4
DOI	https://doi.org/10.1016/j.matpur.2017.05.002
出版状态	已出版 - 10月 2017
已对外发布	是

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10.1016/j.matpur.2017.05.002

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title = "The Oort conjecture on Shimura curves in the Torelli locus of hyperelliptic curves",

abstract = "Oort has conjectured that there do not exist Shimura varieties of dimension >0 contained generically in the Torelli locus of genus-g curves when g is sufficiently large. In this paper we prove the analogue of this conjecture for Shimura curves with respect to the hyperelliptic Torelli locus of genus g>7.",

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author = "Xin Lu and Kang Zuo",

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AU - Lu, Xin

AU - Zuo, Kang

PY - 2017/10

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N2 - Oort has conjectured that there do not exist Shimura varieties of dimension >0 contained generically in the Torelli locus of genus-g curves when g is sufficiently large. In this paper we prove the analogue of this conjecture for Shimura curves with respect to the hyperelliptic Torelli locus of genus g>7.

AB - Oort has conjectured that there do not exist Shimura varieties of dimension >0 contained generically in the Torelli locus of genus-g curves when g is sufficiently large. In this paper we prove the analogue of this conjecture for Shimura curves with respect to the hyperelliptic Torelli locus of genus g>7.

KW - Complex multiplication

KW - Hyperelliptic curves

KW - Shimura curves

KW - Torelli locus

UR - https://www.scopus.com/pages/publications/85021398107

U2 - 10.1016/j.matpur.2017.05.002

DO - 10.1016/j.matpur.2017.05.002

M3 - 文章

AN - SCOPUS:85021398107

SN - 0021-7824

VL - 108

SP - 532

EP - 552

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 4

ER -

The Oort conjecture on Shimura curves in the Torelli locus of hyperelliptic curves

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