PreprintarXiv licencearXiv
Toric flatness I
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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BibTeX
@misc{lodh2026toric,
title = {{Toric flatness I}},
author = {Rémi Lodh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11326},
eprint = {2610.11326},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11326},
}
RIS
TY - UNPB
TI - Toric flatness I
AU - Rémi Lodh
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11326
UR - https://arxiv.org/abs/2610.11326
AB - 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.
ER -