论文标题
重新审视DWORK协同学：Frobenius Eigenvalues在刚性同胞学中的可见性和划分性
Revisiting Dwork cohomology: Visibility and divisibility of Frobenius eigenvalues in rigid cohomology
论文作者
论文摘要
我们研究了通过DWork方法在有限的$ Q $元素上定义的各种刚性支持的刚性同谋的Frobenius Eigenvalues。这项研究将得出几个算术后果。作为第一个应用，我们表明，有限的许多相关仿射品种的Zeta功能能够见证该品种刚体共同体的所有Frobenius Eigenvalues，以达到潮流。这个结果似乎并不以$ \ ell $ -ADIC的共同体而闻名。作为第二个应用程序，我们证明了该品种刚性共同体的Frobenius特征值的几个$ Q $ - 可见度的下限。这些刚性共同体学的这些划分范围通常比在中间的共同体学维度之前和之后，从$ \ ell $ - ad-adic的共同体中的最著名的划分范围提出的范围都要好。
We study Frobenius eigenvalues of the compactly supported rigid cohomology of a variety defined over a finite field of $q$ elements via Dwork's method. A couple of arithmetic consequences will be drawn from this study. As the first application, we show that the zeta functions for finitely many related affine varieties are capable of witnessing all Frobenius eigenvalues of the rigid cohomology of the variety up to Tate twist. This result does not seem to be known for $\ell$-adic cohomology. As the second application, we prove several $q$-divisibility lower bounds for Frobenius eigenvalues of the rigid cohomology of the variety in terms of the multi-degrees of the defining equations. These divisibility bounds for rigid cohomology are generally better than what is suggested from the best known divisibility bounds in $\ell$-adic cohomology, both before and after the middle cohomological dimension.
