论文标题
Frobenius Eigenvalues在$ \ ell $ -ADIC协同学上的划分性
Divisibility of Frobenius eigenvalues on $\ell$-adic cohomology
论文作者
论文摘要
V2：对于在具有$ Q $元素的有限字段定义的投射品种，显示为代数整数，几何弗罗贝尼乌斯的特征值在$ \ ell $ addic的共同体上作用于$ \ ell $ -Adic的共同体，其比$ q $ q $ $ q $ $ - 可见性。这既促进了Deligne的完整性定理和第一作者和N. Katz证明的共同体学定理。对于超出中间维度的复杂品种的霍奇水平也证明了类似的下限，从而改善了早期的方向。我们讨论仿射案例。以前的版本在这个地方包含差距。我们感谢Dingxin Zhang注意到它。
v2: For a projective variety defined over a finite field with $q$ elements, it is shown that as algebraic integers, the eigenvalues of the geometric Frobenius acting on $\ell$-adic cohomology have higher than known $q$-divisibility beyond the middle dimension. This sharpens both Deligne's integrality theorem and the cohomological divisibility theorem proven by the first author and N. Katz. Similar lower bounds are proved for the Hodge level for a complex variety beyond the middle dimension, improving earlier results in this direction. We discuss the affine case. The previous version contained a gap at this place. We are thankful to Dingxin Zhang for noticing it.
