Remark on nondegeneracy of simple abelian varieties with many endomorphisms

DOI10.1142/S1793042115500657zbMath1322.11064arXiv1301.4005OpenAlexW2171243797MaRDI QIDQ5253880

Rin Sugiyama

Publication date: 5 June 2015

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.4005

zbMATH Keywords

abelian varietyHodge conjectureLefschetz classesTate conjecture

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Complex multiplication and moduli of abelian varieties (11G15)

Cites Work

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• Lower bounds for the ranks of CM types
• Algebraic cycles on Abelian varieties of Fermat type
• Exceptional Hodge classes on certain abelian varieties
• Proof of the Tate conjecture for products of elliptic curves over finite fields
• Lefschetz classes of simple factors of the Jacobian variety of a Fermat curve of prime degree over finite fields
• Lefschetz classes on abelian varieties
• Endomorphisms of Abelian varieties over finite fields
• Good reduction of abelian varieties
• The Tate conjecture for certain abelian varieties over finite fields
• On the Hodge groups of some abelian varieties