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

^*Corresponding author for this work

Johannes Gutenberg University Mainz

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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.

Original language	English
Pages (from-to)	532-552
Number of pages	21
Journal	Journal des Mathematiques Pures et Appliquees
Volume	108
Issue number	4
DOIs	https://doi.org/10.1016/j.matpur.2017.05.002
State	Published - Oct 2017
Externally published	Yes

Keywords

Complex multiplication
Hyperelliptic curves
Shimura curves
Torelli locus

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10.1016/j.matpur.2017.05.002

Cite this

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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",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Masson SAS",

year = "2017",

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doi = "10.1016/j.matpur.2017.05.002",

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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

Abstract

Keywords

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