通过相干函子的多态性的开性
Openness of versality via coherent functors
摘要：
我们使用相干函子证明了多角性的开放性。作为应用，我们简化了Artin的堆栈代数性准则。我们还介绍了多步骤的障碍理论，利用它们来产生障碍理论的堆栈相干层，报价函子，和空间的地图中存在的非平坦性。
英文摘要：
We give a proof of openness of versality using coherent functors. As an application, we streamline Artin's criterion for algebraicity of a stack. We also introduce multi-step obstruction theories, employing them to produce obstruction theories for the stack of coherent sheaves, the Quot functor, and spaces of maps in the presence of non-flatness.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
