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Logarithmic Kunz and Radu--André Theorems
Abstract
Frobenius morphisms play a crucial role in algebraic geometry and commutative algebra in positive characteristic. In particular, \textit{the Kunz theorem}, characterizing non-singularity via Frobenius morphisms, is a monumental work and has a relative version, called \textit{the Radu--André theorem}. In this paper, we extend the Kunz theorem and the Radu--André theorem to logarithmic algebraic geometry in positive characteristic.
Related
- Hilbert-Kunz multiplicities of powers of ideals and normalized Hilbert coefficients
- A uniform effective André--Oort result
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- Aubry-André transition in photonic time quasicrystals
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BibTeX
@misc{takeuchi2026logarithmic,
title = {{Logarithmic Kunz and Radu--André Theorems}},
author = {Ryoma Takeuchi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16307},
eprint = {2610.16307},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16307},
}
RIS
TY - UNPB
TI - Logarithmic Kunz and Radu--André Theorems
AU - Ryoma Takeuchi
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16307
UR - https://arxiv.org/abs/2610.16307
AB - Frobenius morphisms play a crucial role in algebraic geometry and commutative algebra in positive characteristic. In particular, \textit{the Kunz theorem}, characterizing non-singularity via Frobenius morphisms, is a monumental work and has a relative version, called \textit{the Radu--André theorem}. In this paper, we extend the Kunz theorem and the Radu--André theorem to logarithmic algebraic geometry in positive characteristic.
ER -