论文标题
在有限田和扭转的共同体中，卡拉比野三倍
Calabi-Yau threefolds over finite fields and torsion in cohomologies
论文作者
论文摘要
我们研究了有限领域的三倍的Calabi-yau三倍的例子。特别是，我们为K. Joshi的猜想提供了一个反例，以将Calabi-yau提升为特征为零。我们还计算了由Cynk-van Straten构建的一些Calabi-yau三倍的P-Adic共同体，该阶层具有显着的算术特性，以及Hirokado三倍的P-Van Straten。这些示例和计算回答了B. Bhatt，T。Ekedahl，van der Geer-Katsura和Patakfalvi-Zdanowicz的一些杰出问题，并为Beauville-Bogomolov分解带来了积极特征的新灯。我们的工具包括P-Adic Hodge理论以及古典代数拓扑。我们还提供了潜在的示例，表明在阳性特征中的三倍的杂物数不是衍生的，与特征零的情况相反。
We study various examples of Calabi-Yau threefolds over finite fields. In particular, we provide a counterexample to a conjecture of K. Joshi on lifting Calabi-Yau threefolds to characteristic zero. We also compute the p-adic cohomologies of some Calabi-Yau threefolds constructed by Cynk-van Straten which have remarkable arithmetic properties, as well as those of the Hirokado threefold. These examples and computations answer some outstanding questions of B. Bhatt, T. Ekedahl, van der Geer-Katsura and Patakfalvi-Zdanowicz, and shed new light on the Beauville-Bogomolov decomposition in positive characteristic. Our tools include p-adic Hodge theory as well as classical algebraic topology. We also give potential examples showing that Hodge numbers of threefolds in positive characteristic are not derived invariants, contrary to the case of characteristic zero.
