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arXiv · 2610.11326

Toric flatness I

Rémi Lodh
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Abstract

We establish some basic properties of t-flat fine log schemes, i.e., fine log schemes whose underlying schemes are flat over their log structure (in a suitable sense). Notably, we show that the depth of a t-flat fs log scheme is simply determined by its logarithmic stratification. We also show that there is a good theory of log cotangent complexes for t-flat fine log schemes, and use the log cotangent complex to give a homological criterion for t-flatness.

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Rémi Lodh. 2026-10-08. Toric flatness I. https://arxiv.org/abs/2610.11326

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