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August 2007 Abelian varieties over $\mathbf{Q}$ associated with an imaginary quadratic field
Tetsuo Nakamura
Proc. Japan Acad. Ser. A Math. Sci. 83(8): 152-156 (August 2007). DOI: 10.3792/pjaa.83.152

Abstract

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 $\mathbf{Q}$.

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Tetsuo Nakamura. "Abelian varieties over $\mathbf{Q}$ associated with an imaginary quadratic field." Proc. Japan Acad. Ser. A Math. Sci. 83 (8) 152 - 156, August 2007. https://doi.org/10.3792/pjaa.83.152

Information

Published: August 2007
First available in Project Euclid: 22 January 2008

zbMATH: 1206.11076
MathSciNet: MR2371522
Digital Object Identifier: 10.3792/pjaa.83.152

Subjects:
Primary: 11G05 , 11G10 , 11G15

Keywords: abelian variety , Complex Multiplication , ellptic curve , Hecke character

Rights: Copyright © 2007 The Japan Academy

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Vol.83 • No. 8 • August 2007
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