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April 2022 On nondegenerate CM-types
Masanari Kida
Rocky Mountain J. Math. 52(2): 547-566 (April 2022). DOI: 10.1216/rmj.2022.52.547

Abstract

We study bounds of the rank of CM-types of CM-fields, and using the bounds, we show that all CM-types of Galois CM-fields with cyclic or dicyclic Galois groups of order 2kp with a prime p are nondegenerate. We also show the nondegeneracy of CM-types for certain non-Galois CM-fields. As a consequence, the Hodge conjecture is true for abelian varieties with complex multiplication by such CM-fields.

Citation

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Masanari Kida. "On nondegenerate CM-types." Rocky Mountain J. Math. 52 (2) 547 - 566, April 2022. https://doi.org/10.1216/rmj.2022.52.547

Information

Received: 4 April 2021; Revised: 2 July 2021; Accepted: 12 July 2021; Published: April 2022
First available in Project Euclid: 17 May 2022

Digital Object Identifier: 10.1216/rmj.2022.52.547

Subjects:
Primary: 11G15 , 14K22
Secondary: 12F12

Keywords: CM abelian variety , CM-type , dicyclic extension , Hodge conjecture

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 2 • April 2022
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