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Endomorphism algebras of factors of certain hypergeometric Jacobians


Authors: Jiangwei Xue and Chia-Fu Yu
Journal: Trans. Amer. Math. Soc. 367 (2015), 8071-8106
MSC (2010): Primary 14H40, 11G15
DOI: https://doi.org/10.1090/tran/6330
Published electronically: April 3, 2015
MathSciNet review: 3391910
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Abstract: We classify the endomorphism algebras of factors of the Jacobians of certain hypergeometric curves over a field of characteristic zero. Other than a few exceptional cases, the endomorphism algebras turn out to be either a cyclotomic field $ E=\mathbb{Q}(\zeta _q)$, or a quadratic extension of $ E$, or $ E\oplus E$. This result may be viewed as a generalization of the well known results of the classification of endomorphism algebras of elliptic curves over $ \mathbb{C}$.


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Additional Information

Jiangwei Xue
Affiliation: Institute of Mathematics, Academia Sinica, 6F, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan, Republic of China
Address at time of publication: Collaborative Innovation Centre of Mathematics, School of Mathematics and Statistics, Wuhan University, Luojiashan, Wuhan, Hubei, People’s Republic of China, 430072
Email: xue_j@math.sinica.edu.tw, xue_j@whu.edu.cn

Chia-Fu Yu
Affiliation: Institute of Mathematics, Academia Sinica, 6F, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan, Republic of China
Email: chiafu@math.sinica.edu.tw

DOI: https://doi.org/10.1090/tran/6330
Keywords: Hypergeometric curves, endomorphism algebras, Jacobians
Received by editor(s): April 23, 2013
Received by editor(s) in revised form: April 25, 2013, and September 4, 2013
Published electronically: April 3, 2015
Article copyright: © Copyright 2015 American Mathematical Society