log纯度，根堆栈上的torsors与log Nori基本群
Log purity, torsors on root stacks and log Nori fundamental group
AI总结：
本文基于log纯度定理，推广至Kummer log flat拓扑下的torsors，并通过根堆栈解释，将其与tame代数堆的properness准则联系，最终构造log Nori基本群方案以分类torsors并进行比较。
摘要：
我们把Fujiwara-Kato-Mochizuki的log纯度定理推广到由Kummer log flat拓扑下有限平坦线性可约群方案产生的torsors。然后通过根堆栈给出纯度定理的堆栈解释，将其与Bresciani-Vistoli对 tame代数堆的properness准则联系起来。最后，我们构造了一个log regular log scheme的log Nori基本群方案，以分类此类torsors，并将其与经典Nori基本群和tame基本群进行比较。
英文摘要：
We generalize the logarithmic purity theorem of Fujiwara-Kato-Mochizuki to torsors which arise in the Kummer log flat topology under finite flat linearly reductive group schemes. We then give a stack-theoretic interpretation of our purity theorem via root stacks, relating it to the valuative criterion of properness for tame algebraic stacks of Bresciani-Vistoli. Finally, we construct a logarithmic Nori fundamental group scheme of a log regular log scheme classifying such torsors, and compare it with the classical Nori fundamental group and the tame fundamental group.
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