The index of degeneracy of a CM abelian variety can be arbitrarily large
Volume 202 / 2022
Acta Arithmetica 202 (2022), 55-66
MSC: 11G15, 14K22.
DOI: 10.4064/aa210515-18-8
Published online: 15 December 2021
Abstract
For a simple abelian variety $A$, the index of degeneracy is the minimum $k$ such that the product $A^k$ holds an exceptional Hodge cycle. We show that for any positive integer $k$ there exists an abelian variety of CM-type with index of degeneracy $k$.
