Log purity, torsors on root stacks and log Nori fundamental group

Sara Mehidi

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arXiv · 2603.23697

Log purity, torsors on root stacks and log Nori fundamental group

Sara Mehidi

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Abstract

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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Sara Mehidi. 2026-03-24. Log purity, torsors on root stacks and log Nori fundamental group. https://arxiv.org/abs/2603.23697

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