本文利用阿贝尔 n 重上的割线层证明判别式 -1 的 Weil 型阿贝尔六重上 Weil 类的代数性，并经退化论证推出阿贝尔四重情形及 Hodge 猜想。
摘要：
A. Weil 在每个具有适当虚二次域复乘法的 2n 维阿贝尔簇的中间上同调中，识别出一个二维的 Hodge 型 (n,n) 有理类空间。这些阿贝尔簇被称为 Weil 型，而这些 Hodge 类被称为 Weil 类。我们证明，对于所有虚二次域，判别式为 -1 的所有 Weil 型阿贝尔六重上的 Weil 类都是代数的。借助 C. Schoen 的退化论证，可推出所有 Weil 型阿贝尔四重（对所有判别式和所有虚二次域）上 Weil 类的代数性。已知阿贝尔四重的 Hodge 猜想可由上述结果推出。
英文摘要：
A. 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.
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