Proceedings of the Japan Academy, Series A, Mathematical Sciences

Abelian varieties over $\mathbf{Q}$ associated with an imaginary quadratic field

Tetsuo Nakamura

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For an imaginary quadratic field $K$ with class number $h$, we shall characterize $h$-dimensional CM abelian varieties over $K$ which descend to abelian varieties over $\mathbf{Q}$. These CM abelian varieties have minimal dimension $h$ both over $K$ and over $\mathbf{Q}$.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 83, Number 8 (2007), 152-156.

First available in Project Euclid: 22 January 2008

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Zentralblatt MATH identifier

Primary: 11G05: Elliptic curves over global fields [See also 14H52] 11G10: Abelian varieties of dimension > 1 [See also 14Kxx] 11G15: Complex multiplication and moduli of abelian varieties [See also 14K22]

abelian variety ellptic curve complex multiplication Hecke character


Nakamura, Tetsuo. Abelian varieties over $\mathbf{Q}$ associated with an imaginary quadratic field. Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 8, 152--156. doi:10.3792/pjaa.83.152.

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