In this article, I give a crystalline characterization of abelian varieties amongst the class of smooth projective varieties with trivial tangent bundles in characteristic $p>0$. Using my characterization, I show that a smooth, projective, ordinary variety with trivial tangent bundle is an abelian variety if and only if its second crystalline cohomology is torsion-free. I also show that a conjecture of KeZheng Li about smooth projective varieties with trivial tangent bundles in characteristic $p>0$ is true for smooth projective surfaces. I give a new proof of a result by Li and prove a refinement of it. Based on my characterization of abelian varieties, I propose modifications of Li’s conjecture, which I expect to be true.

中文翻译：

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具有平凡正切束特征的品种

在这篇文章中，我给出了具有平凡切丛特征的光滑射影簇中的阿贝尔簇的结晶刻画。$p>0$. 使用我的表征，我证明具有平凡正切丛的光滑、射影、普通簇是阿贝尔簇当且仅当它的第二个晶体上同调是无扭的。我还证明了李克政关于特征上具有平凡切丛的光滑射影簇的猜想$p>0$对于光滑的投影表面是正确的。我给出了李的一个结果的新证明，并证明了它的改进。基于我对阿贝尔簇的描述，我提出了对李猜想的修改，我希望它是正确的。