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Log smooth curves over discrete valuation rings

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Abstract

We give necessary and sufficient conditions for log smoothness of a proper regular arithmetic surface with smooth geometrically connected generic fibre over a discrete valuation ring with perfect residue field. As an application, we recover known criteria for log smooth reduction of minimal normal crossings models of curves.

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Notes

  1. It is likely that Y/G is log smooth over V but we won’t need this.

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Acknowledgements

I am indebted to Arne Smeets for raising the question answered by Corollary 4, for useful correspondence and comments on my early results, and for sending me [15], which motivated me to look for Theorem 1. I also thank Lorenzo Ramero and Takeshi Saito for valuable comments. Finally, I am very grateful to the referee, whose comments led to considerable improvements.

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    Rémi Lodh

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  1. Rémi Lodh
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Lodh, R. Log smooth curves over discrete valuation rings. manuscripta math. 167, 197–211 (2022). https://doi.org/10.1007/s00229-020-01268-1

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