Algebraicity of cyclotomic Weil Hodge cycles

Algebraicity of some Weil Hodge classes

We show the dominance of a certain Prym map. By the Scoens result, this implies the algebraicity of Weil Hodge classes of Abelian 6-folds for the Gauss number field with the discriminant 1.

Artin--Hasse--Weil L-级数在整体函数域上的代数性

Algebraicity of Artin--Hasse--Weil L-series over global function fields

本文证明了整体函数域上阿贝尔簇的L-函数被Artin表示扭曲后的特殊值满足Deligne周期猜想的类比，并以椭圆曲线为例说明。

secant sheaves 和 Weil 类 on abelian varieties

Secant sheaves and Weil classes on abelian varieties

本文研究了 abelian 变分上的 secant sheaves 和 Weil 类，通过构造嵌入和极化策略，证明了 Weil 类的 algebraicity，并推导了 Hodge 猜想的结论。

Torsion of abelian varieties, Weil classes and cyclotomic extensions

Let $K$ be a field finitely generated over the field of rational numbers, $K(c)$ the extension of $K$ obtained by adjoining all roots of unity, $L$ an infinite Galois extension of $K$, $X$ an abelian variety defined over $K$. We prove that under certain conditions on $X$ and $K$ the existence of infinitely many L-rational points of finite order on $X$ implies that the intersection of $L$ and $K(c)$ has infinite degree over $K$.

由阿贝尔 n 重上的割线层产生的 Weil 型阿贝尔 2n 重上的闭链

Cycles on abelian 2n-folds of Weil type from secant sheaves on abelian n-folds

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。

McMullen曲线、Weil位移以及Abelian六折的Hodge猜想

McMullen's Curve, the Weil Locus, and the Hodge Conjecture for Abelian Sixfolds

研究McMullen曲线与Weil位移在Abelian六折中的性质，证明其交点为有限且可能为空，揭示Hodge-Weil类的特殊性及Hodge猜想的新案例。