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On CM-types of Galois CM-fields without proper CM-subfields

  • Masanari KidaEmail author
Article
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Abstract

We show that all CM-types of Galois CM-fields without proper CM-subfields are nondegenerate. As a consequence, the Hodge conjecture is true for abelian varieties with complex multiplication by such CM-fields.

Keywords

Complex multiplication CM-type Hodge conjecture CM-field 

Résumé

Nous montrons que tous les corps galoisiens et CM sans sous-corps propre CM possèdent un type CM non-dégénéré. En conséquence, la conjecture de Hodge est vraie pour les variétés abéliennes à multiplication complexe par de tels corps.

Mathematics Subject Classification

11G15 14K22 

Notes

Acknowledgements

This paper grew out of the lectures by Hiromichi Yanai on the theory of complex multiplication at Tokyo University of Science from September 6th to 9th, 2017. The author would like to express sincere gratitude to Professor Yanai for his excellent lectures.

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Copyright information

© Fondation Carl-Herz and Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science Division ITokyo University of ScienceTokyoJapan

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