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BIMSA AG Seminar
Cycles on abelian $2n$-folds of Weil type from secant sheaves on abelian $n$-folds.
Cycles on abelian $2n$-folds of Weil type from secant sheaves on abelian $n$-folds.
演讲者
Eyal Markman
时间
2025年03月27日 10:00 至 11:30
地点
A6-101
线上
Zoom 638 227 8222
(BIMSA)
摘要
In 1977 Weil identified a $2$-dimensional space of rational classes of Hodge type $(n,n)$ in the middle cohomology of every $2n$-dimensional abelian variety with a suitable complex multiplication by an imaginary quadratic number field. These abelian varieties are said to be of Weil type and these Hodge classes are known as Weil classes. We prove that the Weil classes are algebraic for all abelian sixfold of Weil type of discriminant $-1$, for all imaginary quadratic number fields. The algebraicity of the Weil classes follows for all abelian fourfolds of Weil type (for all discriminants and all imaginary quadratic number fields), by a degeneration argument of C. Schoen. The Hodge conjecture for abelian fourfolds is known to follow from the above result.