Endomorphism algebras of factors of certain hypergeometric Jacobians
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- by Jiangwei Xue and Chia-Fu Yu PDF
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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 $\mathbb {C}$.References
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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
- MR Author ID: 899506
- 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
- MR Author ID: 716493
- ORCID: 0000-0003-1634-672X
- Email: chiafu@math.sinica.edu.tw
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 367 (2015), 8071-8106
- MSC (2010): Primary 14H40, 11G15
- DOI: https://doi.org/10.1090/tran/6330
- MathSciNet review: 3391910