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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Jacobians with complex multiplication


Authors: Angel Carocca, Herbert Lange and Rubí E. Rodríguez
Journal: Trans. Amer. Math. Soc. 363 (2011), 6159-6175
MSC (2010): Primary 11G15, 14K22
Published electronically: June 27, 2011
MathSciNet review: 2833548
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Abstract: We construct and study two series of curves whose Jacobians admit complex multiplication. The curves arise as quotients of Galois coverings of the projective line with Galois group metacyclic groups $ G_{q,3}$ of order $ 3q$ with $ q \equiv 1 \mod 3$ an odd prime, and $ G_m$ of order $ 2^{m+1}$. The complex multiplications arise as quotients of double coset algebras of the Galois groups of these coverings. We work out the CM-types and show that the Jacobians are simple abelian varieties.


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Additional Information

Angel Carocca
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306-22, Santiago, Chile
Email: acarocca@mat.puc.cl

Herbert Lange
Affiliation: Mathematisches Institut, Universität Erlangen-Nürnberg, Germany
Email: lange@mi.uni-erlangen.de

Rubí E. Rodríguez
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306-22, Santiago, Chile
Email: rubi@mat.puc.cl

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05560-1
PII: S 0002-9947(2011)05560-1
Keywords: Complex multiplications, Jacobians, abelian varieties
Received by editor(s): May 8, 2009
Published electronically: June 27, 2011
Additional Notes: The first and third authors were supported by Fondecyt grants 1095165 and 1100767, respectively.
Article copyright: © Copyright 2011 American Mathematical Society