论文标题
Hodge标准猜想中的希尔伯特符号
The Hilbert symbol in the Hodge standard conjecture
论文作者
论文摘要
我们研究了承认CM提升的有限场上的品种的Hodge标准猜想，例如Abelian品种或K3表面的产物。对于这些品种，我们表明，该猜想预测的签名符合True Modulo $ 4 $。这相当于确定交叉产品的判别和希尔伯特象征。第一个是由$ \ ell $ -ADIC参数获得的，而第二个则需要在$ p $ -Adic Hodge理论中进行仔细的计算。
We study the Hodge standard conjecture for varieties over finite fields admitting a CM lifting, such as abelian varieties or products of K3 surfaces. For those varieties we show that the signature predicted by the conjecture holds true modulo $4$. This amounts to determining the discriminant and the Hilbert symbol of the intersection product. The first is obtained by $\ell$-adic arguments whereas the second needs a careful computation in $p$-adic Hodge theory.
